In a small saucepan over medium-low heat, combine the white vinegar, sugar, and tomato paste. Stir until the sugar dissolves and the tomato paste loosens completely, then remove from the heat and let it cool slightly.
Wash all produce thoroughly. Peel the onion and peaches, remove the peach pits, and cut the tomatoes, peaches, onion, red bell pepper, and jalapeño into similar-sized chunks.
Place the blade attachment into the food processor first. Layer the chopped ingredients evenly around the blade, reserving the garlic for later. Add the cilantro close to the top so it does not over-process.
Add the lime juice, salt, cumin, and cayenne pepper. Lock the lid firmly into place.
Pulse the salsa in short bursts. While pulsing, drizzle the vinegar mixture through the feed tube. Stop while the salsa still looks chunky and spoonable, not smooth.
Remove the lid and taste. Adjust the salt, sweetness, or cayenne as needed depending on the ripeness of the peaches and your preferred heat level.
Finely mince the garlic by hand and stir it into the salsa after processing.
Transfer the salsa to an airtight container and chill for at least 2 hours before serving.
