Brush a 9" x 9" pan with oil. In a bowl, beat eggs, milk, Parmesan and 1/4 teaspoon each salt and black pepper. Add bread; toss until coated; ransfer to pan; let sit. Heat oven to 400°F. In a large nonstick pan, heat 2 tablespoons oil over medium-high heat. Sauté bell pepper, onion, thyme and remaining 1/2 teaspoon 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 5 minutes. Garnish with thyme, if desired.