In the bowl of a stand mixer fitted with a dough hook (or in a large bowl if mixing and kneading by hand), combine 2 cups of the flour, yeast, salt, herbs, and garlic.
Heat the water and olive oil in a small saucepan until steaming. Remove from heat and let sit for 5 minutes, or until temperature is between 120-130° F. Slowly add the water and oil to the dry ingredients, while mixing on low speed. Use a spatula to scrape down the bowl as needed.
With the mixer on medium low, add the remaining flour a ¼ cup at a time, mixing until incorporated between each addition. Continue adding flour until the dough clears the bowl and is sticky to the touch without coming off in your hands. Knead with a dough hook or by hand until smooth and elastic.
Shape dough into a ball and place in a greased bowl and cover with plastic wrap. Put in a warm place and let rise until doubled, about 1 hour.
Gently push down on the center of the dough to release the gases and knead by hand on a clean surface a few times. Let dough sit for a few minutes, then divide dough in half. Wrap one half in plastic and store for another use (dough will keep in the fridge for 5 days and 2 months in the freezer).
Divide the other half of dough again into 4 pieces. Roll each piece into a rough 6-inch circle. Place on a parchment lined sheet and brush with olive oil. Cover with plastic wrap and let rise for 30 minutes while you prepare the toppings.
To make the pizzas:
In a skillet over the stove, cook the sausage until browned. Transfer to a paper towel lined plate to drain.
Add a tablespoon of olive oil to skillet, followed by the peppers and tomatoes. Season with salt and pepper. Cook over medium high heat until softened, about 5 minutes. Alternatively, you can cook the peppers and tomatoes on the grill until slightly charred.
Preheat the grill to medium high. Gently flip the pizza dough onto the prepared grill, oil-side down. Brush the top with olive oil. Close the grill and let cook for 2-3 minutes. Watch it carefully to make sure it doesn't burn.
Flip the pizzas over and immediately cover with toppings - mozzarella, sausage, peppers and tomatoes. Turn grill off and cover. When cheese is melted, about 2-3 minutes, remove pizzas from the grill. Top with basil leaves and fresh ground pepper.