Chef Todd English uses the signature pizza dough from his restaurant Figs to whip up this panini.
Place a pizza stone on a rack in the lower third of an oven. Heat oven to 500 degrees. On a heavily floured surface, roll out half the dough as thinly as possible into a 10-inch circle. Rub with 2 teaspoons olive oil. Using a pizza peel, transfer the dough to the pizza stone, and bake until the dough puffs and is slightly golden brown, about 2 minutes per side. Repeat the process with remaining dough.
Using a towel, remove the crust from the oven, and place on a cutting board. Top half the crust with fennel, zest, 2 teaspoons olive oil, salt and pepper, lemon juice, 10 basil leaves, and mozzarella. Sprinkle the capers, remaining 5 basil leaves, and 2 teaspoons olive oil over the mozzarella. Season with salt and pepper and a final squeeze of lemon. Fold the crust in half. Using the back of a heavy saute pan, press the panini together. Repeat process with remaining panini.
Return the panini to the oven, and bake until the filling is just warmed through. Transfer the panini from the oven to a cutting board, cut the panini in half on the diagonal, and cut into smaller pieces. Serve immediately.