How to Make It
Preheat oven to 400° F. Cut the top half-inch off the heads of garlic exposing the cloves, and drizzle each with a half-teaspoon of oil, then wrap in a sheet of tin foil.
Line a sheet pan with foil and drizzle with a tablespoon of oil. Put the small florets into a bowl, drizzle with 3 tablespoons of the oil and toss to coat. Lay in a single layer on the sheet pan, and sprinkle evenly with the sugar, then salt. Put the sheet pan in the oven and the garlic packet on the rack next to it and roast for 45-55 minutes, or until the florets are tender and browned, and the garlic is very soft.
While your garlic and cauliflower is roasting, about 15 minutes before you think they will be done, bring a large pot of well-salted water to a boil and cook your pasta according to package directions to al dente. Save 1 cup of the pasta water when you drain.
Squeeze roasted garlic cloves from their skins into small bowl. Using fork, mash garlic to smooth paste, then stir in Calabrian chile. Add the remaining oil to the pasta pot and put over medium high heat. When shimmering, add the garlic chile paste, and sauté just for a few seconds to flavor the oil. When fragrant, deglaze the pan with white wine and reduce by half. Add the stock to the pan and when simmering, stir in the beans, and let them heat through for about one minute, then add the cooked pasta, the cauliflower, ¼ cup cooking water, parsley and mint, and ½ cup cheese, and stir to combine, lowering the heat to low.
Adjust the consistency of the sauce with additional cooking water if needed. Add the cold butter to the pasta and stir until it emulsifies into the sauce, then gently stir in the lemon supremes and any of their juice that has collected in the bowl. Season with salt and pepper to taste. Serve immediately, sprinkling with remaining ½ cup cheese and toasted nuts, garnish with more parsley, and serve with lemon wedges.