In a large, heavy-bottomed pot or Dutch oven, bring 4 quarts of salted water to a rolling boil. In a medium pot, bring 2 quarts of salted water to a simmer. In a large bowl, prepare an ice bath. In a small bowl, beat together the eggs, cheeses, and garlic, and set aside.

While the water is heating, heat the olive oil over medium heat until it has the consistency of water when rolled in the pan (do not let it smoke or the carbonara will have an acrid flavor). Add the diced bacon, and cook, stirring occasionally, until crisp and brown, about 8 minutes.

While the bacon is crisping, blanch the vegetables in the smaller pot of simmering water. Add the turnips first; then, after 1 minute, add the carrots, and after 30 additional seconds, add the peas. Once the peas have been in the water 30 seconds, drain the vegetables and plunge them into the ice bath to stop the cooking and keep them brightly colored and crisp. Allow to sit in the ice bath for 3 to 4 minutes, then remove and let drain at room temperature.

When the bacon is crisp and browned, add the wine to the bacon and olive oil. Cook while stirring until the wine has reduced slightly, 5 to 6 minutes. Remove from heat, and set aside.

Cook the spaghetti 1 minute less than package instructions. Reserve ½ cup of pasta water before draining the pasta. Put spaghetti back into the warm cooking pot, but keep pot off the heat. Pour the egg and cheese mixture over the hot pasta, sprinkle with the salt, black pepper, and a tablespoon or two of the reserved pasta water. Stir well, making sure to pull the spaghetti up from the bottom of the pot so it is evenly coated in sauce.

Add the bacon mixture and the blanched vegetables. Stir again, and add pasta water and additional ground pepper until the consistency and flavor are to your liking (you will likely have leftover pasta water). Serve immediately.