Bring a large pot of salted water to a rolling boil. Zest and juice two lemons, mince three cloves of garlic, rinse two tablespoons of capers, and chop parsley. Cut salmon fillets into even pieces.

Cook the angel hair pasta according to package instructions (typically 4-6 minutes). Reserve half a cup of pasta water before draining.

Combine flour, salt, and pepper in a shallow dish. Dredge one side of each salmon piece in the flour.

Heat olive oil in a skillet over medium-high heat. Sear salmon pieces floured-side down for 2.5-3 minutes until golden brown. Flip and cook for another 2-4 minutes until cooked through.

Remove salmon from the skillet. Deglaze with lemon juice, add garlic and dairy-free butter, stirring until melted. Mix in broth and capers, simmer for 1-2 minutes.

Return salmon to skillet, spoon sauce over it, and warm together for 1-2 minutes.

Serve pasta on plates, top with salmon and sauce, and garnish with parsley.