Bruschetta With Sautéed Sweet Peppers

Brush both sides of toasts with 3 tablespoons oil. Heat 3 tablespoons more oil, bell peppers, onions, and 1⁄2 teaspoon salt in 12-inch skillet over medium-high heat; cook, stirring occasionally, until vegetables are softened and browned at the edges, 10 to 12 minutes. Reduce heat to medium, push vegetables to sides of skillet, and add remaining 1 teaspoon oil, garlic, and red pepper flakes to center of skillet. Cook, mashing garlic with wooden spoon, until fragrant, about 30 seconds, then stir into vegetables. Reduce heat to low and stir in tomatoes, reserved juice, and thyme. Cover and cook, stirring occasionally, until moisture has evaporated, 15 to 18 minutes. Off heat, stir in vinegar and remaining 1⁄4 teaspoon salt. Divide pepper mixture evenly among toasts, top with shaved Parmesan, and serve.