To make the cheese, drain and rinse the cashews and place them in a high-powered blender along with the remaining mozzarella ingredients. Blend until completely smooth. Transfer to a saucepan placed over medium heat, stirring the cheese constantly. Within 1-2 minutes the cheese will start to get very thick. Keep stirring until the cheese begins to move together while stirring. Remove from heat and let cool while preparing the other ingredients.
To make the sauce, heat the oil in a small saucepan over medium heat. Add onion and garlic and sauté for 4-5 minutes. Stir in the remaining ingredients and bring to a simmer. Let simmer for 10 minutes.
Meanwhile, heat the grill to about 550 degrees. Brush the pizza doughs with olive oil and grill one side of the pizza for 1-2 minutes. Flip the crusts and evenly top with tomato sauce, Roma tomatoes, and spoonfuls of mozzarella.
Put the lid on the grill and cook for about 3 more minutes. The pizza is done when the edges are crisp and dark.
Remove from grill, top with basil and red pepper flakes and serve immediately.