Prepare a grill for diffused indirect heat by building the hot coals evenly around the perimeter of the grill. Remove the center ring from the grill grate and insert a medium cast-iron skillet. Invert another larger cast-iron skillet over the top. This acts as a pizza oven for your outdoor grill. (If using a gas grill, heat to medium-high heat.)
For the pizza dough: Add the flour, honey, salt and yeast to a food processor and pulse a few times to combine. Then add 1 3/4 cups room temperature water and the olive oil and pulse again until the dough comes together into a rough ball and rides around the bowl. Transfer the dough to a lightly floured surface and knead a few times until a smooth elastic ball forms. Divide the dough into 3 equal pieces and place each in a quart-sized deli container or gallon-sized resealable plastic bag with a drizzle of olive oil. Allow to sit at room temperature for 1 hour, then refrigerate overnight and up to 5 days. This makes enough for 3 pizzas. Save the extra dough in the freezer for another time. It will last up to 2 months.
When ready to use, remove the dough from the refrigerator and take it out of its storage vessel while still cold. Allow the dough to rest at room temperature for 1 hour before grilling.
For the cheese mixture: In the meantime, combine the ricotta, mozzarella, pecorino and herbs in a large bowl. Season with salt and pepper.
To make the pizza: Dust a pizza peel or the back of a baking sheet with flour. Press one dough ball out on to the peel, shaping it into a circle. Slide the pizza onto the inverted cast-iron and dollop the cheese mixture over the surface. Scatter the asparagus, onions and Parmesan evenly over the surface and drizzle with olive oil. Cover the grill and bake until golden brown and crusty, 10 to 15 minutes.
Using the peel, remove the pizza from the grill and slide it onto a cutting board. Drizzle with more olive oil, slice and serve with more freshly grated Parmesan over the top.
(Alternatively, you can slide the pizza onto an upside-down sheet tray in the oven and cook in a 500 degrees F oven until golden brown and crusty, 10 to 15 minutes.)