While your grill preheats, prepare all your ingredients: mince the garlic clove and set aside, cut the basil into thin ribbons (chiffonade), halve the cherry tomatoes lengthwise, and pat the drained peaches completely dry with paper towels—this is crucial for getting good grill marks and caramelization. In a small bowl, combine the minced garlic, cherry tomatoes, 2 tablespoons of the olive oil, salt, pepper, balsamic glaze, and honey. Let this mixture sit while you grill; the flavors will meld beautifully. I like to prepare this topping ahead because it allows the tomatoes to release their juices and creates a more cohesive, flavorful topping.
Heat your grill to medium-high heat (around 400°F if using a gas grill). While it preheats, brush both sides of the sourdough slices and all the peach slices with the remaining 1 tablespoon of olive oil. This prevents sticking and helps achieve beautiful caramelization on the grill.
Place the peach slices on the grill first and cook for 2-3 minutes per side until they develop golden-brown grill marks and caramelize slightly. Transfer the grilled peaches to a plate. Then grill the bread slices for 1-2 minutes per side until they're golden and crispy with visible grill marks, being careful not to burn them. The peaches will continue to warm while you finish the bread.
In a small bowl, combine the non-dairy cream cheese with 1 teaspoon of honey and a pinch of salt. Stir until smooth and spreadable. I find that non-dairy cream cheese can be a bit firm, so letting it sit at room temperature for a few minutes before mixing makes it much easier to work with.
Spread a generous layer of the creamy cheese mixture from Step 4 onto each warm grilled bread slice. Arrange the grilled peaches from Step 3 on top of the cheese, then spoon the tomato and garlic mixture from Step 1 (including all the flavorful oils and juices) over the peaches. Finish by scattering the fresh basil chiffonade over each bruschetta. Serve immediately while the bread is still warm and crispy.