Grilled Vegetable and Pesto Flatbread

Name: Grilled Vegetable and Pesto Flatbread
Ingredients: 1.5 teaspoons active dry yeast; 3/4 cup warm water (not hot) 105-115 degrees Farenheit; 1 teaspoon honey; 2 cups whole wheat flour (white whole wheat flour can be used); 1 teaspoon sea salt; 3 tablespoons extra virgin olive oil (divided); 2-4 tablespoons all-purpose flour; 8 ounces cremini mushrooms, sliced; 3 cloves garlic, minced; 1 large beefsteak tomato; 1/2 teaspoon red pepper flakes, optional; 3 ounces Pecorino Romano, cut from a block