Dice the peaches: Wash, dry, and pit the peaches. Cut each into 1/4-inch (6mm) pieces and transfer to a large mixing bowl.
Make the peach topping: Add 2 tablespoons olive oil, balsamic vinegar, honey, lemon juice, minced garlic, salt, and pepper. Stir gently, taste, and adjust as needed. Let rest for 5-10 minutes.
Chiffonade the basil: Stack, roll, and slice the basil leaves into thin ribbons. Set aside and do not add to the peach mixture yet.
Toast the baguette: Preheat broiler to high or oven to 400°F (200°C). Slice baguette diagonally into 1/2-inch thick pieces. Brush with remaining olive oil and toast until golden and crisp.
Rub with garlic: While the toast is still warm, rub the cut side of the remaining garlic clove firmly across the top surface of each slice.
Add basil to topping: Gently stir the basil ribbons into the peach mixture just before serving.
Assemble: If using, spread a thin layer of ricotta or burrata on each toast. Top generously with the peach mixture, using a slotted spoon to avoid excess liquid.
Finish and serve: Arrange on a platter, drizzle with additional balsamic glaze, sprinkle with flaky sea salt, and serve immediately.