Pat the swordfish steaks dry with paper towels. Season both sides with salt and black pepper, then lightly dust with all-purpose flour.
In a large skillet, heat the olive oil and 1 tablespoon of the butter over medium-high heat. Add the swordfish and sear for 3 to 4 minutes per side until golden brown and the internal temperature reaches 145°F. Transfer the fish to a plate and cover loosely to keep warm.
Reduce the skillet heat to medium. Add the minced garlic and cook for 30 seconds until fragrant. Pour in the broth, scraping up any browned bits from the pan. Simmer for about 2 minutes until reduced by half.
Stir in the lemon juice, capers, and heavy cream. Let simmer for 1 minute to slightly thicken.
Remove the skillet from the heat. Swirl in the remaining 2 tablespoons of butter and the chopped parsley until smooth.
While preparing the sauce, quickly steam or sauté the asparagus until tender-crisp.
Serve the warm swordfish alongside the asparagus and pour the warm pan sauce generously over the top.