Pre-heat the oven to 375ºF.
Bring a large pot of water to a boil for the pasta; add salt and cook the pasta to al dente. Meanwhile, heat 2 tablespoons EVOO, two turns of the pan, in a large skillet over medium heat. Add the bacon or pancetta and render to crisp. Add lots of pepper and the garlic and stir for 2-3 minutes. Add the wine and zest.
When the pasta is about done, remove and reserve 1 cup of the starchy cooking water. Remove another 1/2 cup of the starchy cooking water and use it to temper the egg yolks.
Add the parsley to the sauce. Drain the pasta and add it to the sauce. Pour the tempered egg yolks over top and add the cheese; toss for 1-2 minutes to combine (use some of the reserved starchy cooking water if the pasta tightens up too much before a glossy coating forms).
Spray a 6-cup muffin tin with cooking spray. Using tongs, twirl the spaghetti into the cups, making a “nest.” Crack an egg into each one, making sure it stays whole (if you’re worried about breaking the egg yolk, crack the egg into a small bowl first, then pour it in the muffin cup).
Season the tops of the eggs with salt and freshly ground black pepper and place the muffin tin on a baking sheet. Transfer the sheet to the oven and bake for 15 minutes, until the eggs set.