Preheat oven to 375F.
Bring a large pot of water to a boil for the pasta; add salt and cook pasta to al dente.
Meanwhile, heat 2 tablespoons EVOO, 2 turns of the pan, in a large skillet over medium heat. Add bacon or pancetta and render to crisp. Add lots of pepper, garlic and stir 2-3 minutes. Add wine and zest.
When pasta is about done, remove and reserve 1 cup starchy cooking water. Remove another 1/2 cup starchy water and use it to temper the egg yolks.
Add parsley to sauce. Drain pasta and add it to sauce. Pour tempered egg yolks over top and the cheese; toss 1-2 minutes to combine (use some of the reserved cooking water if pasta tightens up too much before 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 youre 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 sheet to the oven and bake 15 minutes, until the eggs set.