Heat a large pot of water to boil for spaghetti.
For the Arrabbiata sauce, heat a large skillet or Dutch oven over medium heat with EVOO, 4 turns of the pan, add onion, garlic, salt, marjoram or oregano, chili paste or chili flakes, and tomato paste, and cook to soften 7-8 minutes. Add wine and cook down 2 minutes, then add sugar, sauce, tomatoes and basil, and simmer 20-30 minutes.
For pasta, in a small pot, heat EVOO, about 3 tablespoons, over medium heat, then add butter and when it foams add garlic and swirl a minute or 2.
Season pasta water liberally with salt, about 2 tablespoons, and cook pasta about 7 minutes. Reserve ¾ cup water and drain pasta, then return to hot pot. Add EVOO and garlic butter, reserved water, Parmigiano-Reggiano, and egg, and toss 2 minutes.
Heat two small 8- to 10-inch nonstick skillets over medium-high heat. Using a fork, twist a large nest, about ¼ of the pasta, and transfer to the nonstick skillet. Cover pan and cook pasta to crisp on bottom and sides but still tender on top. Transfer to warm oven, and repeat. If you’d like the nests crispy on both sides, flip nest over and cook until brown. Place nests in shallow bowl or rimmed dinner plates and top with even layer of sauce and basil. Add fried or over-easy egg, optional.