Pat the monkfish fillets very dry with kitchen paper.
Season both sides of each fillet generously with sea salt and freshly ground black pepper.
Heat the frying pan over medium–high heat until hot, then add the olive oil and swirl to coat.
Carefully place the fillets in the pan and cook undisturbed for 4–5 minutes, until golden brown and edges turn opaque.
Flip the fillets and cook for another 4–5 minutes, until the fish is opaque through and a thermometer reads 63°C in the thickest part.
Remove the cooked fillets to a warm plate and reduce the pan heat to medium.
Add the butter to the pan and let it melt and sizzle gently.
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 pan and spoon the lemon–garlic butter sauce over the fillets.
Sprinkle with the chopped parsley and serve immediately with lemon wedges, new potatoes and steamed green beans or asparagus.