Prep the peppers: Heat your oven to 400°F (200°C).
Slice the tops off the peppers, remove seeds and membranes, and place them upright in a baking dish. Drizzle with olive oil and a pinch of salt. Bake for 12–15 minutes until slightly softened.
Set aside.
Sauté aromatics: In a large skillet over medium heat, add the olive oil. Cook the onion for 3–4 minutes until translucent. Stir in the garlic and cook 30 seconds until fragrant.
Soften the broccoli: Add the chopped broccoli to the skillet with a splash of water.
Cook 3–4 minutes until bright green and crisp-tender. Season with a little salt and pepper.
Build the filling: Reduce heat to low. Stir in the cooked chicken and rice.
Add the chicken broth, Greek yogurt (or sour cream), Dijon, smoked paprika, and Italian seasoning. Mix until creamy and combined. Fold in 1 cup cheddar and the mozzarella.
Taste and adjust salt and pepper.
Stuff the peppers: Spoon the filling into the pre-baked peppers, packing it down lightly. Top each pepper with a generous sprinkle of cheddar.
Bake: Return the dish to the oven and bake 15–18 minutes, until the cheese is melted and lightly golden and the peppers are tender.
Finish and serve: Let the peppers rest 5 minutes. Garnish with chopped parsley.
Serve warm.