Place dough on a lightly floured work surface and let sit at room temperature for 30 minutes. (Skip this step with store-bought crust.)
Salt zucchini discs 1 hour ahead in strainer to remove excess water. (This helps zucchini brown while grilling.)
Ricotta mixture: Mix ricotta, lemon zest, salt, and pepper. Set aside.
Grill or sauté the zucchini for two minutes per side. Set aside.
Heat grill to the highest temperature (600 degrees F, if possible).
Roll out pizza dough to create oblong, organic shape.
Brush one side of dough with olive oil.
Grill dough: Lay dough on grill with olive-oil side down. Brush top of dough with thin layer of olive oil. Let dough cook for about 3 minutes with the lid off, or 1 to 2 minutes with the lid on. Use tongs to lift dough periodically to prevent scorching. The dough should have grill marks on it, but it should not get crispy.
Remove dough from grill.
Top pizza: Spread the grilled side of the dough with a thin layer of ricotta mixture. Layer mozzarella slices evenly, then top with zucchini. Drizzle lightly with olive oil.
Cook pizza: Return topped pizza to the grill and cook with the lid on for about 3 minutes. Use your sense of smell—if pizza smells like it’s scorching, take lid off and move pizza to a cooler part of grill or turn heat down.
Remove from oven and garnish with prosciutto, and basil.