Slice the peaches into 1/2-inch wedges and pat them dry with paper towels—this helps them develop a nice caramelized exterior when grilled. Slice the mozzarella log into rounds and arrange on a plate. Pick the fresh basil leaves and set aside. Measure out the lemon zest, hot honey, balsamic glaze, flaky sea salt, thyme leaves, and black pepper into small bowls or on a cutting board so everything is ready to go. I like to have all my components prepped before I start cooking so the final assembly happens quickly and the toast doesn't get cold.
Heat a grill pan or cast-iron skillet over medium-high heat and lightly brush with 1/2 tablespoon of the olive oil. Once the pan is hot, place the peach wedges directly on the grill surface and cook undisturbed for 3-4 minutes until they develop deep golden grill marks. Flip and grill the other side for another 2-3 minutes until caramelized and tender. The peaches should still hold their shape but have charred edges. Transfer them to a plate and let cool slightly.
Using the same grill pan or a clean skillet, brush both sides of the sourdough slices lightly with 1 tablespoon of unsalted butter. Heat the pan to medium heat and toast the bread for 2-3 minutes per side until golden brown and crispy with light grill marks. The bread should be firm enough to hold toppings but still have a slightly yielding crumb inside.
Place the toasted sourdough slices on a serving plate or cutting board. Layer the grilled peaches from Step 2 onto each slice, followed by the mozzarella rounds from Step 1, distributing them evenly. Scatter the fresh basil leaves over the cheese. Drizzle the remaining 1 1/2 tablespoons of extra virgin olive oil and the balsamic glaze over the toast, then top with the hot honey—I find the hot honey's warmth creates a beautiful contrast when it touches the cool cheese. Finish with a sprinkle of flaky sea salt, fresh thyme leaves, lemon zest, and cracked black pepper.