Preheat oven to 400°F. Stem 6 (5-inch) portobello mushrooms and scrape out gills with a spoon. Brush 1 1/2 Tbsp. olive oil all over mushrooms. Place on a large, rimmed nonstick baking sheet, hollow side up. Bake for 10 minutes and remove from oven. (Leave oven on.)
Using paper towels, blot excess moisture from mushroom cavities and season with salt and pepper. Spread 1 Tbsp. jarred pizza sauce in cavity of each mushroom. Divide 2 oz. sliced turkey pepperoni and 1 green pepper, seeded and thinly sliced, evenly among mushroom caps. Top each with 1/4 cup shredded Italian four-cheese blend.
Return mushrooms to oven and bake until cheese is bubbling, about 10 minutes. Serve hot.