Cook tortellini: boil salted water, cook tortellini until just tender, and reserve at least 1/2 cup pasta water before draining.
Cook bacon: crisp bacon in a large skillet over medium heat. Transfer bacon to a paper towel-lined plate and leave about 2 tablespoons fat in the pan.
Make sauce: whisk eggs, parmesan, black pepper, and salt in a bowl until smooth.
Combine: add hot tortellini to the warm skillet. Remove from heat and stir in the egg mixture quickly.
Loosen: add reserved pasta water, a tablespoon at a time, until the sauce is glossy and creamy.
Finish: stir in bacon and parsley if using. Serve immediately with extra parmesan and black pepper.