Preheat your oven to 400ºF . Line a sheet pan with foil or parchment paper.
In a small mixing bowl whisk together broth, lemon juice, garlic, and hot sauce.
Season the salmon fillets lightly with salt and pepper. Lay salmon fillets (bottom side down) in the sheet pan spacing them evenly apart.
Brush the salmon fillets with the broth/lemon/hot sauce mixture, then top with the diced butter.
Bake the salmon fillets in the preheated oven for 10 to 13 minutes. In the meantime, blanch the green beans in boiling water for 3 minutes (or more if you like them tender), then drain.
Arrange green beans around the roasted salmon fillets and toss them a little into the butter sauce. Return to the oven for 2 or 3 minutes to crisp up. Sprinkle with parsley and serve the garlic butter baked salmon and green beans immediately, garnished with lemon slices.