Heat the oven to 400°F while you prepare the sauce and coating. The oven should be fully hot before the fish goes in so the fillets finish evenly after searing.
Whisk the lemon juice, extra virgin olive oil, and melted butter together in a shallow bowl, leaving out the garlic for now. The mixture should look glossy and lightly blended, with butter and oil floating in small streaks.
Combine the flour, coriander, paprika, cumin, salt, and black pepper in a second shallow bowl. Stir until the spices are evenly distributed and no darker clumps of seasoning remain.
Dry the cod, coat each piece first in the lemon mixture, then in the seasoned flour, and shake away loose excess. A thin, even coating should cover the fish without forming thick patches that can fall away in the pan.
Warm 2 tbsp olive oil in a cast iron skillet or other oven-safe pan over medium-high heat, then sear the cod for about 2 minutes per side. The oil should shimmer, and the coating should turn pale golden while the centers remain undercooked.
Stir the minced garlic into the reserved lemon mixture and spoon it over the seared fillets. The garlic will release a noticeable savory aroma when it meets the warm pan and sauce.
Transfer the skillet to the oven and bake for about 10 minutes, checking early for doneness. The cod is ready when the flesh is opaque and separates into tender flakes with gentle pressure from a fork; scatter with parsley and serve immediately.