Preheat the grill (or grill pan) to medium.
Brush (or toss) the peaches, Roma tomatoes, sweet onion, and jalapeño with olive oil. Sprinkle brown sugar on the flesh of the peaches.
Place the peaches, Roma tomatoes, sweet onion, and jalapeño face down on the grill. Grill the peaches and sweet onion for 4 - 5 minutes per side until grill marks have formed and the peaches are slightly tender. Grill the Roma tomatoes and jalapeño for 3 - 4 minutes per side. Remove and cool.
Place the cherry tomatoes, garlic cloves, cilantro, brown sugar, lemon juice, apple cider vinegar, salt, and pepper into a food processor. Puree for 10 seconds.
Remove the skin from the Roma tomatoes. The tomatoes should be blistered so the skin comes off easily. If not, it's okay to keep the skin on. Roughly chop the peaches (skin on), Roma tomatoes, sweet onion, and jalapeño. This helps blend the salsa effortlessly and more uniformly.
Add all the grilled ingredients into the food processor and puree (or pulse) until you reach desired consistency, about 30 seconds.
Pour the Grilled Peach Salsa into a container and chill in the refrigerator for at least one hour to marinate the flavors. Taste and adjust seasoning as needed.
Serve with your favorite tortilla chips or store in an airtight container in the refrigerator for up to one week. Enjoy!