Preheat oven to 375°. Cook the sausage in a medium skillet over medium-high heat until crumbly and crispy, about 5 minutes. Transfer to a plate lined with paper towels to drain, reserving drippings in the skillet. Add the mushrooms, onion and oil to the skillet, and cook until the vegetables are softened, about 5 minutes. Transfer the mushroom mixture to a bowl and add the sausage, mozzarella, pepperoni, basil, red peppers and 1/2 teaspoon of the oregano; stir to combine.
Separate the biscuit dough. Using a rolling pin, roll out each biscuit on a lightly floured surface until the biscuits triple in size (about 5 inches in diameter). Brush the edges of the dough rounds with a small amount of beaten egg then scoop 1/4 cup of the sausage mixture into the center of each biscuit. Gather the dough edges around the sausage mixture to form a purse, and squeeze to seal. Roll them around gently on the cutting board so they form a ball. Repeat with the remaining biscuits.