Bring a large pot of salted water to a boil. Add the pasta and cook according to package directions until al dente. Reserve 1 cup of pasta water, then drain the pasta.

While pasta cooks, pat salmon cubes dry and season with salt and pepper. Heat olive oil in a large skillet over medium-high heat. Add salmon and cook for 2-3 minutes per side, until golden and cooked through. Remove salmon from the skillet.

In the same skillet, melt butter over medium heat. Add garlic and cook until fragrant, about 30 seconds. Pour in heavy cream, bring to a simmer, and cook for 2-3 minutes until it thickens slightly.

Stir in Parmesan cheese until smooth. Add spinach and cook until wilted. Stir in lemon juice and red pepper flakes. Return cooked pasta and salmon to the skillet. Toss to combine, adding reserved pasta water as needed to reach desired sauce consistency. Serve immediately.