Wash and trim the ends of the asparagus, then blanch them in boiling water for 2- 3 minutes then soak in ice water to stop cooking. This way they will cook faster and evenly in the skillet. You can skip this step if you have very thin asparagus. Drain and set aside.
Heat olive oil in a large cast iron skillet over medium-low heat. Gently cook salmon on both sides until golden brown. Remove the salmon fillets from the skillet and set aside to a plate.
In the same skillet over medium heat, add minced garlic then deglaze with vegetable broth (or wine). Bring to a simmer. Add butter, lemon juice, hot sauce, parsley. Give a quick stir to combine.
Add the drained blanched asparagus and toss for 2 minutes to cook it up. Add salmon back to the pan and reheat for another minute. Garnish with more parsley, crushed chili pepper, and lemon slices and serve the garlic butter salmon and lemon asparagus immediately. Enjoy!