Preheat the oven. Set it to 400°F (200°C).
Line a baking sheet or a 9x13-inch dish with parchment for easy cleanup.
Prep the peppers. Slice peppers in half lengthwise, keeping stems intact if possible. Scoop out seeds and membranes. Brush with a little olive oil and season with salt and pepper.
Place cut-side up in the baking dish.
Par-bake the peppers. Roast for 10–12 minutes to soften slightly. This step ensures the peppers are tender by the time the filling is hot and bubbly.
Sauté aromatics. While the peppers bake, heat olive oil in a skillet over medium. Add onion and cook 3–4 minutes until translucent.
Stir in garlic and red pepper flakes; cook 30 seconds until fragrant.
Build the sauce. Add Italian seasoning and chicken broth. Simmer 2–3 minutes to reduce slightly.
Make it creamy. Lower the heat and stir in cream cheese until smooth. Remove from heat and mix in Greek yogurt or sour cream, 1/2 cup Parmesan, lemon juice, and zest.
Add chicken and herbs. Fold in the shredded chicken and parsley.
Taste and season with salt and black pepper. The filling should be creamy but scoopable; add a splash of broth if too thick.
Stuff the peppers. Spoon the mixture into each par-baked pepper half. Top with mozzarella and the remaining 1/4 cup Parmesan for a golden, cheesy crust.
Bake to finish. Return to the oven for 12–15 minutes, until the cheese is melted and lightly browned and the peppers are fork-tender.
Rest and serve. Let peppers rest for 5 minutes so the filling sets.
Garnish with extra parsley and a crack of black pepper.