Bring a large pot of salted water to a boil. Add the linguine and cook until al dente according to package directions. Reserve 1 cup of pasta water, then drain the rest and set the pasta and pasta water aside.
In a large skillet over medium heat, add olive oil. Once hot and shimmering, add the sliced kielbasa in a single layer and cook for 4 to 5 minutes, stirring occasionally, until browned and slightly crisp on the edges. Depending on the size of your skillet, you may need to work in batches. Transfer kielbasa to a plate and set aside.
Reduce heat to medium-low. In the same skillet you browned the kielbasa, add butter and minced garlic. Cook for about 30 seconds, stirring frequently.
Stir in the hoisin sauce, soy sauce, and sriracha. Slowly pour in the heavy cream, whisking until smooth. Let the sauce warm through for 1 to 2 minutes.
Add the cooked linguine to the skillet and toss to coat in the sauce.
Stir in the parmesan cheese until melted and creamy. If needed, add a splash of reserved pasta water, a little at a time, to loosen the sauce. (I added ¼ cup pasta water.)
Return the kielbasa to the skillet and toss everything together until heated through, about 1 to 2 minutes.
Serve warm, topped with extra parmesan, chopped parsley, and freshly squeezed lemon juice, if desired.