Pat the monkfish fillets very dry with paper towels.
Season both sides of each fillet generously with sea salt and freshly ground black pepper.
Heat a large skillet over medium-high heat until hot, then add the olive oil and swirl to coat.
Carefully place the fillets in the skillet and cook undisturbed for 4–5 minutes, until they’re golden brown and the edges look opaque.
Flip the fillets and cook for another 4–5 minutes, until the fish is opaque throughout and a thermometer inserted into the thickest part reads 145°F.
Transfer the cooked fillets to a warm plate and reduce the heat to medium.
Add the butter to the skillet and let it melt, then add the chopped garlic and cook for about 30 seconds, until fragrant but not browned.
Pour in the dry white wine (or vegetable stock) and simmer for 1–2 minutes, scraping up any browned bits.
Stir in the fresh lemon juice.
Return the monkfish to the skillet and spoon the lemon-garlic butter sauce over the fillets.
Sprinkle with chopped parsley and serve immediately with lemon wedges, baby potatoes, and steamed green beans or asparagus.