Stuffed Portobello Mushrooms

Name: Stuffed Portobello Mushrooms
Ingredients: 1 tbsp olive oil, divided; 4 medium-sized portobello mushrooms; 2 chicken breasts (or 2 cups leftover cooked chicken); 1/2 red pepper, diced; 1/2 red onion, diced; 1 egg; 1/4 cup breadcrumbs; 2 cloves garlic, minced; 1/2 tsp each salt & pepper; 1/4 cup fresh parsley, chopped; 1 cup shredded cheddar cheese, divided