Bring a large pot of salted water to a boil. Add the pasta to the water and cook until al dente. Remove 1 cup of the starchy pasta water from the pot before straining the pasta. Set pasta aside, but try to keep the pasta warm.
Next, add the eggs, whole milk, and pecorino cheese to a large bowl and whisk until combined. Slowly drizzle ¼ cup of the warm (not hot) pasta water into the egg mixture, whisking constantly until combined. Be sure the pasta water is not hot, or it will scramble the eggs. Set aside.
Heat a large Dutch oven over medium/high heat. Add the pancetta to the Dutch oven and cook for 4-5 minutes until partially cooked.
Add the onion and garlic and season with salt. Sauté for 1-2 minutes, and then add the garlic. Cook for an additional 1 minute.
Deglaze the Dutch oven with white wine. Pour the wine into the pan and scrape the brown bits from the bottom of the pan. Then, whisk the anchovy paste into the white wine.
Add the cooked spaghetti to the Dutch oven and toss it with all of the ingredients.
Remove the Dutch oven from the heat and let it cool for 2-3 minutes.
Once the pot has had time to cool, slowly pour the egg and cheese mixture over the pasta and constantly stir to be sure the egg doesn’t scramble.
When the egg mixture becomes creamy and warm, serve with cracked pepper, shredded cheese, and chopped parsley. Be sure the Dutch oven isn’t hot, or else the eggs will scramble.