For the stew:
8 tablespoons (1 stick) unsalted butter, divided
7 large yellow onions (5 to 5 1/2 pounds total), halved and cut into 1/4-inch-thick slices
4 large shallots (about 8 ounces), peeled and cut into small dice
4 teaspoons kosher salt, divided
1 teaspoon freshly ground black pepper, divided
6 cloves garlic, minced
5 stalks celery (about 12 ounces), including leaves, cut into small dice
5 carrots (about 8 ounces), peeled and cut into small dice
6 cups cremini and/or button mushrooms (about 1 1/2 pounds), sliced thinly
Cooking spray
1/4 cup all-purpose flour
1 cup dry Riesling wine
6 to 8 fresh sage leaves, minced, or 2 teaspoons dried sage
Leaves of 5 sprigs fresh thyme, finely chopped
1 (15-ounce) can white beans and their liquid (optional)

For the topping:
1 large baguette (about 1 pound), cut crosswise into 24 slices
12 ounces Gruyere, Comté, or Raclette cheese, shredded
4 tablespoons unsalted butter