The Parmesan toasts are slices of broiled baguette. Cut as many slices of bread as there are servings. If you don’t want to use the broiler for the bread, put them in a toaster, then put them on a baking sheet, sprinkle with Parmesan and heat in the oven until the cheese is melted.
4 T olive oil, divided
2 medium onions, chopped fine
3 garlic cloves, minced
10 c thinly sliced cabbage
7 c broth
salt and pepper, to taste
6 slices bread cut from a baguette or other elongated loaf (about 3/4-inch thick)
6 T grated Parmesan cheese, plus extra for the table
1. Heat 2 T of the olive in in a large casserole or Dutch oven. Add the onions and sauté over medium heat until golden, about 7 minutes. Add the garlic and continue cooking until garlic is fragrant, about 1 minute.
2. Add the cabbage to the pot and stir to coat with the oil. Cook until slightly wilted, about 5 minutes. Add the broth, salt, and pepper. Bring to a boil, reduce the heat to medium-low, cover, and simmer until the cabbage is tender, anywhere from 20 minutes to about 1 hour, depending on the type and age of the cabbage you are using. Taste for seasonings.
3. When the soup is almost ready, preheat the broiler. Brush the remaining 2 T of oil over both sides of the bread slices. Place the bread on a baking sheet and broil until crisp on the first side. Remove the baking sheet from the oven, turn the bread slices, and sprinkle the cheese over the untoasted side of the bread slices. Return the baking sheet to the broiler and broil until the bread is crisp on the second side and the cheese has melted. Watch carefully to make sure the bread does not burn.
4. Ladle the soup into individual bowls. Float one toast slice, cheese side up, in each bowl. Serve immediately, passing extra grated cheese at the table.