Start by preheating your oven to 400°F. Cut the peppers in half lengthwise then remove the seeds and inner membrane.
Mix cream cheese, chives, salt and pepper in a bowl and stir in the broccoli florets until well combined.
Spoon the filling into the pepper halves, being careful not to overstuff the peppers or you'll have the filling falling out on all sides.
Place the peppers on a foil-lined baking sheet and bake until the filling is heated through and the peppers are soft, for 9 to 11 minutes. Sprinkle with cheddar cheese and then bake another three to four minutes longer until the cheese is melted. Let the peppers cool slightly before serving.
