In a large pot of boiling salted water, cook linguine, stirring occasionally, until al dente according to package directions. Drain.
In a large skillet over medium-high heat, heat oil. Add sausage and cook, turning occasionally, until seared on both sides, about 2 minutes per side. Add garlic and cook, stirring, until fragrant, about 1 minute more. Stir in tomatoes, cream, and Parmesan; season with salt and pepper. Bring mixture to a low boil, then reduce heat to medium. Cook, stirring frequently, until sauce is slightly thickened, about 5 minutes.
Add pasta and spinach to skillet and toss until pasta is fully coated in sauce and spinach is wilted, 2 to 3 minutes. Top with basil and more Parmesan.