Bring a large pot of salted water to a boil and cook the pasta until al dente according to package directions. Reserve a small cup of pasta cooking water, then drain the pasta.
Season the salmon with salt and pepper, then lightly coat all sides with flour, shaking off any excess.
Heat the olive oil and 2 tablespoons butter in a skillet over medium-high heat until hot and butter is melted.
Add the salmon to the skillet and cook about 2 minutes per side until seared; remove the salmon to a plate and set aside. If salmon has skin and you prefer not to serve it, peel the skin off now.
Reduce heat to medium and add the chicken or vegetable broth, minced garlic, and lemon juice to the skillet. Simmer for about 1 minute to combine and slightly reduce the sauce.
Return the salmon to the pan and break it into bite-size pieces with a spoon. Cook a few more minutes until the salmon is fully cooked and the sauce has reduced to your liking.
Add the drained pasta to the skillet and toss to coat, adding a splash of reserved pasta water if needed to loosen the sauce. Serve immediately with optional parsley, red pepper flakes, and parmesan.
