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1
Heat 2 tablespoons of the oil and the butter in a large pot with a tightfitting lid over medium heat until the butter foams.
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2
Add the celery and onion and cook, stirring occasionally, until softened.
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3
Add the garlic and fennel and cook, stirring occasionally, until softened.
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4
Add the yellow squash and zucchini, season with salt, and cook, stirring occasionally, until softened.
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5
Add enough water to cover the vegetables by 1 inch and bring to a boil.
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6
Add the cauliflower and green beans and stir to combine.
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7
Add the kale, spinach, and escarole, stirring until the greens begin to wilt, and return to a boil.
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8
Add more water as needed to cover the vegetables by about an inch of liquid.
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9
Reduce the heat to low, cover, and simmer until all of the vegetables start to soften, about 20 minutes.
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10
Add the remaining olive oil and the bouillon cubes and stir until the bouillon cubes have dissolved.
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11
Cover and continue cooking until the vegetables are completely softened, the soup thickens slightly, and the flavors have melded, about 1 hour.
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12
Taste and season with salt or additional bouillon cubes as needed.
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13
Keep warm.
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14
Heat the oven to 300 degrees F and arrange a rack in the middle.
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15
Place half of the bread slices on a work surface and spread with half of the mayonnaise.
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16
Flip the bread slices over and evenly divide the cheese among the slices.
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17
Spread the remaining bread slices with the remaining mayonnaise and place them mayonnaise-side up over the cheese to form 10 sandwiches.
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18
Heat a large nonstick frying pan or griddle over medium-low heat until hot, about 4 to 5 minutes.
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19
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.
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20
Flip the sandwiches and cook until the second sides are golden brown and the cheese is completely melted, about 5 minutes more.
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21
Transfer to a baking sheet and place in the oven to keep warm.
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22
Repeat with the remaining sandwiches.
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23
When all the sandwiches are cooked, remove the baking sheet from the oven and place on a wire rack.
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24
Let cool 1 to 2 minutes before cutting each sandwich in half.
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25
Ladle the soup into bowls and sprinkle with pepper.
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26
Serve with the grilled cheese sandwiches.