Place your pizza stone in the oven and preheat to 425°F.
Toss the carrots with the olive oil and roast for 15-20 minutes until tender with lightly caramelized edges.
Increase the oven temperature to its highest setting (500-550°F) and allow the pizza stone to continue heating for another 30 minutes.
While the oven heats, sauté the mushrooms in a skillet over medium-high heat until they release their moisture and begin to brown. Stir in the thyme leaves during the final minute of cooking.
Stretch the pizza dough.
Brush the outer edge of the dough with olive oil and sprinkle with the Parmesan, rosemary, and a pinch of flaky salt.
Spread a thin layer of carrot top pesto over the dough, leaving the outer edge exposed.
Scatter the Gruyère evenly over the pesto.
Arrange the roasted carrots and sautéed mushrooms over the cheese.
Bake until the crust is deeply golden and the cheese is bubbling.
Remove the pizza from the oven and immediately top with the prosciutto and small dollops of goat cheese.
Finish with fresh lemon zest and serve.