Prep the asparagus. Rinse, pat dry, and snap off the woody ends.
Thicker spears are great for pan-cooking, but thin ones work too—just shorten the cook time.
Pat the salmon dry. This helps it sear instead of steam. Season both sides with salt and pepper. If you like, sprinkle paprika for color and a hint of warmth.
Heat the pan. Set a large skillet (cast iron or stainless steel) over medium-high heat.
Add olive oil and let it shimmer. You want a hot surface for a good sear.
Sear the salmon skin-side down. Place the fillets in the pan, skin-side down if using skin-on. Press gently with a spatula for the first 20 seconds to prevent curling.
Cook without moving for 4–5 minutes, until the skin is crisp and the sides of the salmon are turning opaque about halfway up.
Add the asparagus. Tuck the spears around the salmon in the same pan. Drizzle a little more olive oil if the pan looks dry. Season the asparagus with salt and pepper.
Flip and baste. Flip the salmon carefully.
Drop in the butter and minced garlic. As the butter melts, tilt the pan and spoon the garlicky butter over the salmon and asparagus for 1–2 minutes. Add lemon zest and a squeeze of lemon juice to the butter to brighten everything.
Finish to your liking. Cook until the salmon is just opaque and flakes easily with a fork, 2–4 minutes more depending on thickness.
For medium, aim for an internal temperature of 125–130°F (52–54°C). For well-done, go to 140°F (60°C), but be careful not to dry it out.
Add heat if you like. Sprinkle in red pepper flakes to the butter during the last minute if you want a little kick.
Rest and garnish. Take the pan off the heat and let the salmon rest for 2 minutes. Shower with chopped parsley or dill.
Serve with extra lemon wedges and spoon the remaining garlic butter over the top.