Step 1

Position racks in middle and upper thirds of oven; preheat to 450 degrees F. Coat a rimmed baking sheet with cooking spray.

Step 2

Heat 2 tablespoons oil and butter in a large pot over medium-high heat. Add sweet and red onions and stir to coat. Cover, reduce heat to medium and cook, stirring often and scraping up any browned bits, until golden brown, 25 to 30 minutes.

Step 3

Meanwhile, place mushrooms caps, gill-side up, on the prepared pan. Brush with 1 tablespoon oil and sprinkle with 1/4 teaspoon pepper. Roast on the middle rack until tender, 10 to 15 minutes. Remove from oven and preheat broiler to high.

Step 4

Add garlic and thyme to the onions and cook, uncovered, for 2 minutes more. Stir in sherry, salt and the remaining 1/4 teaspoon pepper; increase heat to medium-high and bring to a simmer. Cook, stirring often, until most of the liquid has evaporated, about 1 minute. Stir in broth and return to a simmer. Reduce heat and simmer for 10 minutes.

Step 5

Meanwhile, combine Gruyère, breadcrumbs, chives and the remaining 1 tablespoon oil in a small bowl. Divide the mixture among the mushroom caps. Broil the mushrooms until the filling is lightly browned, about 1 minute.

Step 6

Divide the soup among 4 bowls and serve topped with a mushroom "toast."