Bell Pepper and Goat Cheese Strata

2 tablespoons olive oil, plus additional for brushing pan
8 eggs
1 cup milk
1/4 cup grated Parmesan
3/4 teaspoon kosher salt, divided
1/2 teaspoon freshly ground black pepper, divided
8 ounces whole-wheat baguette, preferably day-old, cut into 1-inch cubes
1 large red bell pepper, thinly sliced
1 onion, thinly sliced
1/2 tsp chopped fresh thyme (or 1/4 teaspoon dried)
1/2 cup goat cheese, crumbled
Fresh thyme sprigs for garnish (optional)

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; transfer 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.