Boil a large pot of water. Stir in kosher salt.
Whisk eggs, Parmesan, and black pepper in a mixing bowl until smooth.
Cook spaghetti until al dente. Reserve 3/4 cup cooking water, then drain.
Crisp bacon in a large skillet over medium heat with olive oil, about 6–8 minutes.
Stir in garlic and cook 30 seconds until fragrant. Reduce heat to low.
Add drained pasta to the skillet. Toss to coat in bacon drippings.
Remove pan from heat. Stream in egg mixture, tossing constantly until creamy.
Splash in hot pasta water as needed to loosen to a glossy sauce.
Taste and adjust pepper. Garnish with parsley and extra cheese. Serve immediately.