Pasta Carbonara

10 slices bacon , cut into 1/2-inch pieces

8 1/2 cups water , divided

4 cloves garlic , minced

1 lb spaghetti or linguine

1 1/4 cups finely grated parmesan cheese , plus more for serving (2 oz)

3 large eggs

1 large egg yolk

1 tsp each salt and pepper , or to taste

Chopped fresh parsley , for garnish