Heat the oven to 375°F. Cut the tops from 4 large bell peppers and finely chop (about 1 cup). Remove and discard the inner membrane and seeds. If needed, trim a little bit off the bottom of each pepper so that it is stable when standing up.
Heat 2 teaspoons of the olive oil in a large cast iron or stainless steel skillet over medium heat until shimmering. Add 2 tablespoons panko breadcrumbs and 1 pinch kosher salt. Cook, stirring often, until golden brown, about 2 minutes. Transfer to a small bowl.
Wipe the skillet clean with paper towels. Heat the remaining 2 tablespoons olive oil in the skillet over medium-high heat until shimmering. Add the chopped bell pepper tops, 1 medium diced yellow onion, 1 teaspoon kosher salt, and ½ teaspoon black pepper. Cook, stirring occasionally, until soft and beginning to brown, 4 to 5 minutes. Stir in 3 minced garlic cloves and cook until fragrant, about 30 seconds.
Add 1 pound ground chicken. Cook, breaking up the meat into smaller pieces with a wooden spoon, until cooked through, 4 to 5 minutes. Stir in 1 ½ cups marinara sauce and cook until the sauce is slightly thickened, about 3 minutes.
Remove the skillet from the heat. Stir in ½ cup of the shredded mozzarella cheese, ⅓ cup finely grated Parmesan cheese, and ½ cup coarsely chopped fresh basil leaves. Taste and season with more kosher salt or black pepper as needed.
Evenly divide the filling among the peppers (about 1 cup each). Arrange the peppers, cut-side up, in an 8x8-inch baking dish. Pour in enough water to just cover the bottom of the baking dish. Cover the baking dish tightly with aluminum foil.
Bake until the peppers are tender and the filling is heated through, about 35 minutes. Uncover and sprinkle with the remaining 1 cup mozzarella cheese and toasted panko.
Return to the oven and bake uncovered until the cheese is melted and browned, 8 to 10 minutes. Garnish with more Parmesan cheese and chopped fresh basil leaves if desired.
