Gabrielle Hamilton's Minestrone Soup with Grilled Cheese Sandwiches

1. 1Heat 2 tablespoons of the oil and the butter in a large pot with a tightfitting lid over medium heat until the butter foams. Add the celery and onion and cook, stirring occasionally, until softened. Add the garlic and fennel and cook, stirring occasionally, until softened. Add the yellow squash and zucchini, season with salt, and cook, stirring occasionally, until softened. Add enough water to cover the vegetables by 1 inch and bring to a boil.
2. 2Add the cauliflower and green beans and stir to combine. Add the kale, spinach, and escarole, stirring until the greens begin to wilt, and return to a boil. Add more water as needed to cover the vegetables by about an inch of liquid. Reduce the heat to low, cover, and simmer until all of the vegetables start to soften, about 20 minutes. Add the remaining olive oil and the bouillon cubes and stir until the bouillon cubes have dissolved.
3. 3Cover and continue cooking until the vegetables are completely softened, the soup thickens slightly, and the flavors have melded, about 1 hour. Taste and season with salt or additional bouillon cubes as needed. Keep warm.

For the grilled cheese sandwiches:

1. 1Heat the oven to 300°F and arrange a rack in the middle.
2. 2Place half of the bread slices on a work surface and spread with half of the mayonnaise. Flip the bread slices over and evenly divide the cheese among the slices.
3. 3Spread the remaining bread slices with the remaining mayonnaise and place them mayonnaise-side up over the cheese to form 10 sandwiches.
4. 4Heat a large nonstick frying pan or griddle over medium-low heat until hot, about 4 to 5 minutes. Place 2 to 3 of the sandwiches in the pan and cook until the bottoms are golden brown and the cheese is starting to melt, about 5 minutes. Flip the sandwiches and cook until the second sides are golden brown and the cheese is completely melted, about 5 minutes more. Transfer to a baking sheet and place in the oven to keep warm. Repeat with the remaining sandwiches.
5. 5When all the sandwiches are cooked, remove the baking sheet from the oven and place on a wire rack. Let cool 1 to 2 minutes before cutting each sandwich in half.

To serve:

1. 1Ladle the soup into bowls and sprinkle with pepper. Serve with the grilled cheese sandwiches.