Heat a grill to medium-high heat and shut the lid. Let the grill heat for 20 minutes.
Add a few glugs of olive oil to a small bowl and season with a pinch of salt.
Add the leeks to a small bowl and drizzle with olive oil. Season with salt and pepper.
Sprinkle your work surface with flour. Flatten the Homemade Pizza Dough with your hands and use your fingertips around the edges to define the crust. Flatten the center and stretch the pizza to a 12-inch round while rotating. You can toss it up into the air to get a nice stretch.
Have all of your sauces, olive oil, toppings and spoons set out on a sheet tray next to your grill. You have to have everything prepped and ready to go when grilling pizzas.
Turn one side of your grill down to medium and keep the other side of the grill on medium-high. Place the dough on the medium-high side of the grill and quickly brush all over with olive oil. Let the dough cook just until the dough is firm on the bottom and has some nice char marks, 1 to 2 minutes. Flip the dough over to the cooler side of the grill by using either a sheet tray turned upside down or a pizza peel.
Brush the other side of the dough with olive oil, then top the pizza. Spread the Broccoli Pesto out from the center, leaving an edge for the crust. Spread out the mozzarella, then evenly distribute the leeks and ricotta cheese. Close the grill and cook until the cheese is melted and the crust is cooked through, about 5 minutes.
Remove with a pizza peel or sheet tray. Place on a cutting board and slice up and serve. Sprinkle with some Parmesan before serving.
Stir the yeast, warm water and honey together in the bottom of a standing mixer bowl. Stir in 1/2 cup of the all-purpose flour. Mix until combined. Let sit until the mixture looks bubbly and foamy and the yeast is activated, about 30 minutes.
Preheat the oven to 200 degrees F. Once the oven is warm, turn it off. Outfit a standing mixer with a dough hook. Oil a large bowl with olive oil.
In a medium bowl, whisk together the remaining 3/4 cups all-purpose flour, the bread flour and salt until well blended.
Turn the mixer on and add the cold water and olive oil to the bubbly yeast mixture. Add the flour by scoopfuls. Knead for 5 minutes until the dough comes together into a ball. Sprinkle some flour down on your cutting board and knead the dough by hand for another minute or so until it's smooth and elastic. Place the dough in the bowl and flip to coat all sides with oil. Cover with a kitchen towel and wait until doubled in size, about 2 hours.
Punch down and let rise again for 1 1/2 more hours.
Split the dough into 2 equal-size balls, cover with a slightly damp tea towel and let rest for 10 minutes before stretching.
Bring a large saucepan of water to a boil. Add a big pinch of salt and stir in the broccoli. Boil the broccoli until very tender, about 5 minutes. Drain the broccoli in a colander in the sink and rinse under very cold water to stop the cooking.
Add the broccoli, Parmesan, pistachios, basil, olive oil and garlic to a food processor and process until smooth. Season the pesto with a small pinch of salt and pepper.