Thinly slice the heirloom tomato and peach into circular pieces. Set these aside.
Put a pan that has a tight-fitting lid on medium heat and add a generous glug of olive oil. Let this heat up before adding in the slices of bread. The bread should sizzle when it hits the pan (of course!)
Drizzle more olive oil on the sides of the bread facing up, and then rub in 1/2 tablespoon of za'atar seasoning on each slice. When the bottoms of the slices are golden brown, flip them over so the za'atar side is on the pan. Turn the heat to low.
Add 2 ounces of burrata to each slice of bread, and quickly cover the pan with its lid. This will steam and melt the cheese.
Let the cheese melt for about 1-2 minutes, and then transfer the toasts to plates.
Top with tomato slices, peach slices and fresh basil. Sprinkle on salt and pepper and eat immediately.