Step 1

Position racks in the upper and lower thirds of the oven and preheat to 450 degrees F.

Step 2

Mix the flour, warm water, 1 1/2 teaspoons kosher salt and the yeast in a stand mixer fitted with a dough hook on low speed until no dry flour remains. Increase the speed to medium-low and knead until the dough is smooth and elastic, about 15 minutes. Scrape down the bowl, cover with plastic wrap and let the dough rise at room temperature until doubled in size, about 1 hour.

Step 3

Meanwhile, spread the pistachios on a baking sheet and bake until toasted, 5 to 7 minutes; let cool. Trim the carrot tops, reserving the greens. Toss the carrots with 2 tablespoons olive oil, 1 teaspoon kosher salt and a few grinds of pepper on a rimmed baking sheet. Arrange the carrots in a single layer and roast on the upper oven rack until just tender, 15 to 20 minutes. Sprinkle with the brown sugar and roast until the carrots start to caramelize, about 10 more minutes. Remove from the oven.

Step 4

Grease a 9-by-13-inch metal baking pan with 1/4 cup olive oil. Punch down the dough using wet hands and transfer to the pan, stretching from corner to corner. Let rise again until doubled in size and bubbly, about 1 hour.

Step 5

Make the pesto: Pulse the pistachios in a food processor until coarsely ground; set aside 2 tablespoons for topping. Add the parsley and garlic to the remaining nuts in the food processor and pulse to combine. Add 3/4 cup carrot greens, the lemon zest and juice and 1/2 teaspoon kosher salt; pulse until chopped. Pulse in the remaining 1/4 cup olive oil. If the pesto is too thick, pulse in water, 1 teaspoon at a time. Season with kosher salt.

Step 6

Drizzle 1/4 cup pesto over the dough; dimple with your fingers, pushing the pesto into the dough. Arrange the carrots on top and sprinkle with 1/2 teaspoon flaky salt. Bake on the lower oven rack until the edges are golden brown, about 15 minutes. Transfer to the upper rack and bake until the top is golden brown, about 10 more minutes. Let cool slightly on a rack.

Step 7

Top the focaccia with the remaining pesto, the reserved pistachios and about 2 tablespoons chopped carrot greens. Cut into small pieces and serve warm.