Preheat oven to 350 degrees.
Bring a large saucepan of water to a simmer.
Place halved peppers in boiling water and cook until soft, about 4 minutes; drain.
Heat the olive oil in a large skillet over medium-high heat; add mushrooms, chili powder, cumin, and garlic powder; cook and stir until mushrooms start to soften about 5 minutes.
Fill cooked peppers with mushroom mixture and top each evenly with cheese; arrange stuffed peppers on a baking sheet and bake until cheese has melted about 10 minutes.