Brown the sausage. Heat 2 Tbsp olive oil over medium-high heat in a large skillet. Add sausage, then use a wooden spoon to break up into smaller pieces. Cook until mostly cooked through and browned on all sides, about 3-5 minutes. Use a slotted spoon to transfer the sausage to a medium bowl.
Sauté the veggies. To the skillet, add sliced fennel and onion. Lower the heat slightly, then cook until they begin to caramelize, about 3-5 minutes.
Season the veggies. Add chopped rosemary, lemon zest, and ¼ tsp red pepper flakes, then stir to combine.
Grate the cheese. Use a food processor to finely grate mozzarella cheese.
Preheat a grill over medium heat until it reaches 375-400°F (190-205°C). For the first phase of cooking, we will use direct heat.
Roll out the pizza dough. While the grill is preheating, use a rolling pin to roll out the pizza dough (or use your hands to press it out into a circle). You can make two small pizzas or one large, family-style pizza. For either, go for a thickness of about ½-¾-inch.
Lightly oil the grill. Make sure the grill grates are clean. Next, use either grill spray to coat the grates lightly or pour some olive oil on a paper towel, then use tongs to gently rub the oil across the grill grates.
Cook the dough on one side. Carefully transfer the pizza dough to the grill. Lay it flat across the grates. If any edges fold or tuck under, use tongs to quickly unfold them. Cook for 3-5 minutes, then use tongs to transfer the partially cooked pizza dough to a rimmed baking sheet. Turn off half the burners on the grill. When the pizza returns, it will be cooked over indirect heat.
Assemble the pizza. Turn a rimmed baking sheet over so that it's upside down. Place partially cooked pizza dough on top, with the grilled side facing up (the uncooked side will have direct contact with the grill during phase two of cooking!). Use a spoon to spread ⅓ cup of marinara sauce evenly on top, leaving the outer 1-inch untouched. Use remaining marinara, if needed. Sprinkle half of the grated mozzarella cheese, then layer on cooked sausage, caramelized onion and fennel, and ½ cup roasted red peppers strips, spreading evenly across the dough. Top with remaining mozzarella cheese.
Return pizza to the grill. Gently slide the pizza (or use flat spatulas / tongs to help transfer) onto the grill, setting the pizza over the burners that have been turned off. Cover and cook until the bottom of the crust is crispy and the cheese has melted, about 5-7 minutes longer. Rotate the pizza halfway through cooking so all sides of the crust cook evenly.
Finish pizza off the grill. Drizzle the pizza with a high quality extra virgin olive oil, then sprinkle with freshly grated Pecorino Romano. Finish by adding ripped basil on top (you can add whole or thinly sliced basil if you prefer!).
Cool, then slice. Allow the pizza to rest for 5 minutes before slicing, then enjoy!