Using your oven: Preheat your oven to 425 degrees. Using a baking sheet, lightly drizzle with olive oil and rub around with your fingers, coating the pan. Place your pizza dough on top and spread gently with your fingers. Cover with a kitchen towel to let the dough rest for about 10 minutes, and then spread the dough with your fingers again.
Spread on the pesto, add the cheese over the top and place and arrange the shaved asparagus on top however you like. Bake in the oven for about 20 to 25 minutes, checking on the pizza after 20 minutes. Remove from the oven and garnish with the basil and crushed red pepper flakes if desired. Slice and enjoy!
If using an outdoor grill: Heat your outdoor gas grill to about 400 to 425 degrees. Brush each side of the pizza dough lightly with extra virgin olive oil and place onto a large baking sheet covered with parchment paper or a non-stick baking mat so it doesn't stick.
Once the grill is ready, place the pizza dough on the hottest part of the grill and close the lid. Check the pizza crust after a minute or so. Once grill marks have appeared and the crust is slightly crispy, flip it using tongs and a large grill spatula. Close the lid and check the crust after a minute or so.
After the pizza crust is grilled just slightly, remove the pizza crust from the grill and close the grill so the grill stays hot. Spread on the pesto over one side of the pizza crust and place back into the hot grill but in a spot that does not have direct heat.
While on the grill, sprinkle on the mozzarella cheese and close the grill. Check the pizza after a minute or so to ensure it is not burning and you have placed the pizza in a good spot. Turn the grill heat down a little if you need to. Close the lid again. After about 4 to 5 minutes, or when the cheese has started to melt, place the shaved asparagus on top and close the lid again. The pizza is finished when the asparagus is warmed through. I prefer a little "bite" to my asparagus so this method worked for me. Alternatively, you can place the shaved asparagus on top and finish the pizza in a 400 degree oven so you can control the temperature better if it's too hard to manage with your grill.
Drizzle on some extra virgin olive oil, season with salt and pepper and sprinkle with lemon zest and finely diced scallions before serving.