Pat the hake fillets dry with paper towels and season both sides with salt and freshly ground black pepper.
Finely mince the garlic and chop the parsley; set aside.
Heat a large nonstick skillet over medium-high heat and add the extra-virgin olive oil.
Once the oil is hot and shimmering (not smoking), arrange the fillets in the pan without overcrowding.
Cook for 3 to 4 minutes per side, until the fish is opaque in the center and flakes easily.
Transfer the fillets to a plate. Reduce the heat to medium, and in the same pan, sauté the minced garlic for about 30 seconds, until fragrant and lightly golden.
Remove the pan from the heat and stir in the chopped parsley.
Serve the fillets immediately, spoon the garlic–parsley mixture over each, and squeeze fresh lemon juice on top.