In a bowl, beat eggs, milk, Parmesan, and 1/4 tsp salt and pepper. Add bread, toss until coated; transfer to pan and let sit.
Heat oven to 400 degrees.
In large nonstick skillet, cook strips of bacon until crisps. Remove and place on paper towel. In same pan (yes with bacon grease), sauté bell pepper, onion, thyme and remaining 1/2 tsp salt and 1/4 tsp black pepper until onion begins to brown, 10 minutes. Add bell pepper mixture to pan; spread evenly over bread mixture; dot with goat cheese.
Bake until top is puffed and browned and center is firm, 25 minutes. Let rest for 5 minutes. Garnish with thyme.