01 - Heat 1 tablespoon olive oil in a large skillet over medium heat. Add the onions and peppers. Sauté for 5–7 minutes, stirring occasionally, until softened. Remove from the pan and set aside.
02 - Add the remaining tablespoon of olive oil to the skillet. Add the sliced mushrooms and cook for 5–7 minutes, until they release their moisture and become golden brown.
03 - Stir in minced garlic, smoked paprika, soy sauce, black pepper, and salt. Cook for 1 minute more. Return the sautéed onions and peppers to the pan. Mix well and cook for another 2 minutes.
04 - In a small saucepan, whisk together soy or oat milk, nutritional yeast, cornstarch, vegan butter, garlic powder, onion powder, turmeric, and salt. Place over medium heat, whisking continuously, until the sauce thickens and becomes creamy (about 3–5 minutes). Remove from heat.
05 - Slice the hoagie rolls lengthwise, without cutting all the way through. Toast lightly if desired.
06 - Fill each roll with the mushroom-pepper mixture. Generously spoon vegan cheese sauce over the filling. Serve immediately while hot.