Preheat your oven to 475°F (245°C). If using a pizza stone, place it in the oven to heat up as well.
On a floured surface, stretch or roll out the pizza dough to your desired thickness, about 12 inches in diameter. Transfer the dough to a floured pizza peel or a baking sheet lined with parchment paper.
Brush a thin layer of olive oil over the pizza dough, ensuring the edges are well coated.
Evenly distribute the sliced peaches over the dough, leaving a small border around the edges for the crust.
Tear the burrata cheese into pieces and place it over the peaches, allowing it to melt slightly in the oven.
Season the pizza with a sprinkle of salt, cracked black pepper, and fresh thyme leaves if using.
Carefully slide the pizza onto the preheated pizza stone or place the baking sheet in the oven. Bake for 10-12 minutes, or until the crust is golden and crispy.
Once baked, remove the pizza from the oven and let it cool for a minute.
Top the warm pizza with fresh arugula and drizzle balsamic glaze over the top.
Slice and serve warm, enjoyed as a delightful mix of flavors.