Bring a large pot of heavily salted water to a boil and cook the pasta to al dente. Drain and reserve at least 1/2 cup of pasta water.
Heat a large pan with 1 tbsp olive oil over medium heat. Add the 3 Italian sausage links and use a spatula to crumble them into small pieces. Allow them to get brown and crisp on all sides, adding the sage leaves about halfway through. Then, use a slotted spoon to remove the cooked sausage and set aside. Lower heat slightly.
To the still hot pan, add 3 anchovy filets. Allow them to sizzle in the pan briefly, then use a spatula to break them apart. As they cook, they will dissolve into a paste.
Once the anchovies are broken down, add the diced onion and stir until it begins to sweat, then add the minced garlic and stir. Cook these until they become soft and fragrant.
Add the heavy cream to the pan along with the sausage and sage mixture. Stir to combine over medium-low heat until well incorporated. Add the cooked pasta to the sauce and stir to combine.
Grate ¼-½ cup parmesan and use the hot pasta water to melt it into the sauce. Stir until well incorporated, adding more pasta water as needed. Taste and season with kosher salt and black pepper. Squeeze in ½ of a lemon.
Serve hot and garnish with more parmesan and fresh sliced chives.