Within the bowl of a stand mixer, whisk collectively flour, thyme, yeast, and salt till mixed. Add ¾ cup (180 grams) heat water, oil, and a pair of teaspoons (14 grams) honey. Utilizing the paddle attachment, beat at low velocity till a shaggy dough varieties, 1 to 2 minutes.
Swap to the dough hook attachment. Beat at medium-low velocity till dough is clean and elastic, 10 to 13 minutes. Dough will probably be barely cheesy however ought to come away from sides of bowl.
Flippantly spray a medium bowl with cooking spray. Place dough in bowl, turning to grease high. Cowl and let stand in a heat, draft-free place (75°F/24°C) till doubled in dimension, 45 minutes to 1 hour.
Place oven rack in backside third of oven. Preheat oven to 450°F (230°C). Place a rimmed baking sheet the wrong way up in oven to preheat for half-hour.
In a medium bowl, stir collectively ricotta, crimson pepper, and remaining 2 teaspoons (14 grams) honey.
Gently punch dough down, and divide in half. Working with one portion of dough at a time, press and flatten right into a 12×9-inch oval or rectangle; place dough on a parchment paper-lined baking sheet. (If dough doesn’t stretch simply, cowl and let stand for 10 minutes after which strive once more.) High with 6 slices mozzarella. Fastidiously slide dough on parchment onto preheated baking sheet.
Bake till crust is golden brown and cheese is melted, 10 to fifteen minutes. Whereas first flatbread is baking, repeat process with remaining dough and remaining cheese.
High sizzling flatbreads with peach slices, and dollop with ricotta combination; high with arugula, thyme, and honey. Serve heat.