To Make the Hazelnut Custard Base
Toast the raw hazelnuts (see notes for roasted hazelnuts) at 350° F for 10 - 12 minutes or until golden brown. Do not burn them, or they will be bitter. Remove the hazelnuts from the oven and rub them in a clean kitchen towel to easily remove the skin.
Finely chop 1 3/4 cups of the hazelnuts in a food processor or blender, reserving 1/4 cup for later use. (If you love nuts in your ice cream, toast more than 2 cups and reserve more than 1/4 cup for later.)
Meanwhile, bring 1 cup of heavy cream, milk, sugar, and salt to a low boil in a medium saucepan over medium heat. Once it comes to a low boil, remove the saucepan from the heat and add the finely chopped hazelnuts. Cover the saucepan and let the hazelnuts steep for at least one hour. While the hazelnuts are steeping, you can make the salted caramel.
Once the hazelnuts are finished steeping, strain the mixture through a fine mesh strainer or cheesecloth into another medium saucepan. I prefer the cheesecloth because I can use my hands to squeeze out as much liquid from the hazelnuts as possible. Discard the hazelnuts and rewarm the hazelnut-infused mixture.
In a separate bowl, whisk the egg yolks. Temper the egg yolks by slowly pouring the warm hazelnut-infused mixture over them while continuously whisking.
Return the hazelnut custard base to the saucepan and cook on medium-low heat. Constantly whisk the custard base until it is smooth and thick. Tip: Coat a spoon in the custard base, then draw a line across the back of the spoon with your fingertip. If the line remains clear, the custard base is ready.
In another separate bowl, add the heavy cream and vanilla extract. Pour the hazelnut custard base through a fine mesh strainer over the bowl of heavy cream and vanilla extract. This ensures a smooth custard base in case you have any bits of cooked eggs.
Stir the hazelnut custard base until thoroughly mixed. Press (cover) plastic wrap on the surface of the custard base to prevent forming a skin layer. Place in the refrigerator and chill. It should be at least 40°F before churning.
To Make the Salted Caramel
Combine the heavy cream, salt, and vanilla extract in a small saucepan on low heat. Do not bring the cream to a boil; only warm it up. You can also microwave the cream in a microwave-safe bowl if you desire.
In a separate stainless steel medium saucepan, make a dry caramel by heating the pan over medium heat. When the saucepan is hot, slowly sprinkle the sugar over the pan. When the sugar crystals melt, add more slowly and repeat until all the sugar is dissolved. The sugar will liquefy (melt) around the edges of the pan first. So carefully stir the sugar around the edges so it cooks evenly and does not burn.
When all the sugar is completely melted, it will slowly (or rapidly if your heat is too high) turn into a golden amber color. Turn off the heat because the sugar will continue to cook. The darker the caramel, the more bitter.
Carefully whisk a little of the heavy cream mixture into the dry caramel. The sugar will bubble when you add the cream, so be careful. Continue to whisk the caramel as you add the rest of the heavy cream. At this time, you can turn the heat up to medium to help dissolve the sugar and thicken the caramel. Do not fret if the caramel seizes. Keep whisking the caramel on medium-low heat. It will melt into a smooth consistency.
Whisk in the butter until the caramel is silky smooth.
Remove the caramel from the heat and let it cool. Transfer it to a container and let it set completely for at least 1 hour. You can also chill it in the fridge.
The homemade salted caramel makes about 1 cup. I typically use 1/4 cup of salted caramel for the Hazelnut Salted Caramel Ice Cream. So you will have plenty of leftovers to drizzle more over the ice cream or enjoy it by the spoonfuls!
To Make the Hazelnut Salted Caramel Ice Cream
Pour the chilled hazelnut custard base into the ice cream machine and churn according to the manufacturer's directions. Typically, it's the lowest speed for 15 minutes, but I check after 12 minutes.
While the custard base is churning, coarsely chop the reserved toasted hazelnuts. Once the ice cream is smooth, thick, and sticks to the machine's arm, add the hazelnuts to the ice cream machine. Turn off the machine and use a spatula to help spread the hazelnuts evenly throughout the ice cream.
Pour 1/3 of the hazelnut ice cream into a freezer-safe container. I like to keep my container in the freezer until it's ready to use, so it's already chilled. Drizzle a heaping tablespoon of salted caramel on top of the ice cream. If the salted caramel is cold, rewarm it to room temperature in the microwave. Then, carefully swirl the salted caramel into the ice cream using a butter knife or skewer. Repeat this step two more times.
Cover and freeze the ice cream for at least 2 hours. When ready, scoop and enjoy with more salted caramel drizzled on top!