Preheat oven to 375°F (190°C).
Slice tops off peppers and remove seeds and membranes.
Heat olive oil in a skillet over medium-high heat.
Add onion and ground turkey; cook until turkey is browned and onion is translucent.
Stir in minced garlic and cook for 1 minute.
Remove from heat and stir in cooked rice, half of the tomato sauce, oregano, salt, and pepper.
Place peppers upright in a baking dish and fill each with the turkey mixture.
Top each pepper with remaining tomato sauce and shredded cheese.
Pour 1/4 cup water into the bottom of the dish and cover with foil.
Bake for 35 minutes, then remove foil and bake for an additional 10 minutes until cheese is bubbly and peppers are tender.