Remove the thick outer skins of the soaked beans and place them in a large pot. Cover them with 2 inches of cold water. Crush and add 2 of the cloves of garlic and 2 of the bay leaves.
1½ cups dried butter beans **, 5 cloves garlic, 4 bay leaves
Place the pot over high heat and bring it to a boil. Add the salt and simmer for 1-2 hours or until the beans are very soft. Remove the aromatics, drain the beans, and set them aside.
1 tsp kosher salt
When the beans are almost finished, start the tomato sauce. Heat the olive oil in a large deep skillet until shimmering. Add the shallots and a generous pinch of salt. Sauté until just softened. Mince the remaining garlic and add it. Stir in crushed red pepper flakes, tomato paste, and the Calabrian chilies as well. Sauté for a minute more.
5 cloves garlic, 3 shallots, 3 Calabrian chilies packed in oil, 1 tsp crushed red pepper flakes, 1 tbsp tomato paste
Deglaze the pan with the white wine and stir in the whole canned tomatoes. Break the tomatoes up with the back of your spoon and bring the mixture up to a boil. Add the thyme and the remaining bay leaves and reduce to a simmer. Let cook for 20 minutes.
1 can whole tomatoes, 3 sprigs fresh thyme, 4 bay leaves
Once the 20 minutes have passed, remove the thyme and bay leaves and transfer the sauce to a food processor. Blitz until smooth. Return the sauce to the skillet and add the beans and Swiss chard. Stir in the lemon juice and place over low heat. Cook until the Swiss chard wilts, about 10 minutes.
1 bunch swiss chard, 1 lemon
While the sauce is on its final simmer, wipe out the pot you used to cook the beans and fill it with water. Bring the water up to a boil and liberally salt it before adding the bucatini. Cook until the pasta is al dente. Drain the pasta reserving 1/2 cup of the pasta water. Add the bucatini and pasta water to the simmer sauce and toss to coat.
454g (1lb) dried bucatini
While the pasta is cooking, fill a non-stick skillet 2/3 of the way with water and place over high heat. Bring the water to a boil and reduce to the barest simmer. Stir in the vinegar and crack an egg into a ramekin. Using a spoon, swirl the water to create a small vortex before bringing the ramekin to the surface of the water and dropping the egg in. Repeat with the remaining eggs. Cover and simmer for 3 minutes or until the whites are just set but the yolks are still jiggly. Transfer the eggs to a plate lined with a paper towel to drain.
4 large eggs, 1 tsp white vinegar
Divide the pasta across four plates and top each plate with an egg and garnish with cheese, salt and pepper, and fresh thyme. Serve immediately.
Parmigiano Reggiano, Salt and pepper, additional fresh thyme