For the pizza dough: Mix together the flour, salt and yeast in a bowl, then stir in 350 grams (1 1/2 cups) water until combined. Cover with plastic wrap and put it down for an 18- to 24-hour nap at room temperature until it's doubled in sized and bubbling.
For the pizza toppings: Preheat the grill with a pizza stone over medium-high heat. (If you don't have a pizza stone, you can use a baking sheet.)
Combine the pine nuts, garlic, basil, mint, crushed red pepper, juice of half a lemon, 1/4 teaspoon salt, a few turns of black pepper and the Parmesan in a food processor and pulse to a coarse crumb. With the processor running, drizzle in the olive oil and blend until smooth. Taste and adjust the seasonings as desired.
Divide the pizza dough in half. On a floured pizza peel or baking sheet, flatten out one half of the dough into a 10- to 11-inch round. Spread with a thin layer of the pesto and top with half of the mozzarella. Bring it out to the grill. Grill the zucchini and remaining lemon half on the grates until charred, a few minutes. Add half the zucchini to the pizza and slide it onto the pizza stone. Close the grill and cook until the bottom is browned and cheese is melty, 6 to 9 minutes. Drizzle with more pesto, squeeze with juice from the charred lemon and add more Parmesan, crushed red pepper and basil and serve.
Repeat with the other half of the pizza dough and ingredients.