Pat the shrimp dry with paper towels and set aside. Trim the asparagus and cut the stalks into 3–4-inch pieces.
Melt 1 tablespoon butter in a large skillet over medium heat.
Add the sliced shallot and asparagus. Season lightly with salt and sauté for about 4 minutes, stirring occasionally, until the asparagus is bright green and just fork-tender.
Transfer the asparagus and shallot to a plate and set aside.
Melt the remaining 3 tablespoons butter in the same skillet.
Add the shrimp, minced garlic, and lemon slices. Season lightly with salt.
Cook the shrimp for approximately 2–3 minutes per side, depending on their size, until pink, opaque, and cooked through. Avoid overcooking.
Remove the skillet from the heat. Immediately return the asparagus and shallots to the pan.
Add the fresh lemon juice and chopped parsley. Toss gently until the shrimp and vegetables are coated in the garlic butter sauce.
Taste the 15-Minute Garlic Butter Shrimp and Asparagus and season with additional salt and freshly ground black pepper as needed.
Serve immediately while the shrimp and garlic butter sauce are hot.