Dry and Season the Salmon: Pat the salmon fillets thoroughly dry on all sides with paper towels (moisture is the enemy of a crisp sear). Season both sides generously with kosher salt and freshly cracked black pepper.
Sear the Salmon: Heat 1 tablespoon of olive oil in a large 12-inch heavy-bottomed cast-iron skillet over medium-high heat until shimmering. Carefully lay the salmon fillets flesh-side down (or skin-side down first if preferred) away from you. Sear undisturbed for 4 to 5 minutes until a deeply golden caramelized crust forms.
Flip and Add Asparagus: Gently flip the fillets over. Push them to one side of the skillet. Add the remaining 1 tablespoon of olive oil and the trimmed asparagus spears to the empty side. Season asparagus with a pinch of salt and pepper. Sauté for 3 to 4 minutes, turning occasionally.
Create the Lemon Garlic Herb Butter: Reduce the heat to medium-low. Add the cubed butter, minced garlic, and lemon wheels directly into the center of the skillet. As the butter melts and foams, tilt the pan slightly and use a large spoon to baste the hot, foaming garlic butter continuously over the salmon and asparagus for 1 to 2 minutes.
Add Lemon Juice and Herbs: Squeeze in 2 tablespoons of fresh lemon juice and scatter the chopped fresh dill and parsley into the sizzling butter sauce. Swirl the skillet gently to emulsify the pan juices into a glossy sauce. Remove from heat immediately so the salmon remains tender and flaky (internal temperature 125-130°F for medium).
Plate and Serve: Arrange the tender garlic-herb asparagus spears on warm plates, rest a crispy salmon fillet atop, and spoon the remaining golden pan sauce generously over top. Garnish with charred lemon wheels and flaky sea salt.