Preheat oven to 375°F. Holding a portobello in 1 hand, use a small spoon to gently scrape out gills from underside. Repeat with rest of mushrooms. Sprinkle with salt and pepper. Place portobellos flat, gill side down, on a large baking sheet; bake until slightly softened and just beginning to give off liquid, 10 to 15 minutes. (Time will vary according to size of portobellos.) Pat gill side dry with paper towels.
Warm oil in a large skillet over medium-high heat. Cook onion, stirring, until softened, 3 to 5 minutes. Add garlic; sauté 1 minute more. Add sausage and cook, breaking up large pieces, until no longer pink, 5 to 7 minutes. Stir in tomatoes and increase heat to high. Cook, stirring, until liquid has evaporated, 10 to 12 minutes. Stir in oregano and red pepper. Season with salt and pepper.
Divide sausage mixture among portobellos, filling gill side of each with about 1/2 cup. Top with mozzarella. Bake until cooked through and cheese is melted, about 10 minutes. Serve immediately.