Cook bacon in a large skillet over medium heat. Turn bacon a few times while cooking to get it evenly crisp and crunchy.Remove bacon from pan and set aside on a paper towel.
While bacon is cooking, peel and core the Brussels sprouts, discarding the cores and collecting the leaves in a bowl.
Increase skillet to medium-high and stir-fry Brussels sprouts leaves in bacon fat, tossing and stirring them gently until lightly charred and wilted, approximately 3-4 minutes.Remove from skillet, place in a small bowl, set aside. Turn off the burner, but leave the skillet on the stove, you’ll need it again later.
Bring a large pot of water to a boil over high heat. Cook pasta according to package directions.
While pasta cooks, whisk together milk, eggs, salt, pepper, and parmesan cheese in a medium bowl. When the pasta is almost done cooking, scoop ¼ cup of the pasta water from the pot and slowly drizzle it into into the egg mixture, whisking constantly. Take your time here — if you pour the hot water too quickly, your eggs will scramble!
When pasta has finished cooking, lift pasta directly from the pot into the egg mixture, stirring and tossing to coat the pasta. Chop bacon into small pieces and stir half of it into the pasta and egg mixture.
Return skillet to low heat. Transfer pasta and egg mixture to remaining bacon drippings and cook, stirring constantly, 2-3 minutes, until sauce thickens. Add Brussels sprouts leaves and toss to combine.
Distribute pasta evenly between bowls, sprinkle remaining chopped bacon on top. Grate additional parmesan cheese over the top to serve.