Drain the soaked beans and rinse. Place in a large pot and add water to cover by 2 inches. Bring to a boil over high heat. Adjust heat to maintain a gentle simmer, cover and cook until tender, 1 to 1 1/2 hours.
Meanwhile, preheat oven to 350°F. Line the bottom of a 9-by-13-inch baking dish with parchment paper.
Whisk eggs, parsley, Parmesan, flour and 1/4 teaspoon salt in a large bowl. Pour into the prepared baking dish. Bake until firm, about 15 minutes. Loosen the edges with a spatula. While still warm, invert onto a cutting board. Remove the parchment and cut the frittata into 1/4-inch cubes.
Heat oil in the pot over medium heat. Add onion and garlic and cook, stirring frequently, until the onion is translucent, 5 to 8 minutes. Stir in broth, scraping up any browned bits. Increase heat to high and bring to a boil.
Add escarole, the beans and the 1/4 teaspoon salt and pepper. Return to a boil. Cook until the escarole is just tender, 3 to 5 minutes. Serve the soup topped with the egg "croutons".
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