Step 1

For the crust: In the bowl of a stand mixer, sprinkle the yeast and sugar over the warm water. Whisk to combine and then let sit until bubbles have formed on the surface, about 5 minutes. Add the flour, salt, and 1 tablespoon of the olive oil and mix with the dough hook on low speed until the dough comes together, about 2 minutes. Scrape the bottoms and sides of the bowl. Increase the speed to medium-low and mix until everything is well incorporated and the dough is sticky, 2 to 3 minutes more.

Step 2

Drizzle the top of the dough and down the sides of the bowl with the remaining 1 tablespoon olive oil. Flip the dough to coat in the oil. Cover the bowl with plastic wrap or a clean kitchen towel and let it rise until doubled, about 1 hour 30 minutes.

Step 3

For the pizza: About 30 minutes before you're ready to make the pizzas, place a pizza stone, steel, or an upside-down baking sheet on the upper third rack of the oven and preheat to 500°F. Cover an upside-down baking sheet with a 14-inch piece of heavy-duty foil. Lightly brush the foil with olive oil and dust with flour.

Step 4

On a lightly floured surface, cut the dough in half and shape into tight balls. (If you're making the dough in advance, stop here and see the tip for dough storage below.) Place the balls about 3 inches apart on a lightly floured surface, cover, and let rest until the dough has relaxed and springs back slowly when gently pressed with a finger, about 10 minutes.

Step 5

On a lightly floured surface, pull and stretch one of the dough balls into a 10-inch round and transfer it to the prepared baking sheet. (Keep the other dough ball covered.)

Step 6

Brush the crust with olive oil (including the edges). Working in this order, sprinkle the crust with half the parmesan, garlic, shallots, low-moisture mozzarella, and fresh mozzarella. Top with half the lemon slices and brush them with olive oil.

Step 7

Using the upside-down baking sheet as a pizza peel, slide the pizza with the foil onto the preheated baking stone. Bake until the crust is browned, the cheese is bubbling, and the edges of the lemon are caramelized, 12 to 16 minutes. Drizzle with half the honey and sprinkle with half the basil just before serving. Repeat with the remaining dough and ingredients.