Pat the fish dry and season lightly with salt and pepper. This is the part where you reveal you’re serious about flavor.
Heat olive oil in a skillet over medium heat. When it shimmers, lay in the fish and sear about 2–3 minutes per side until lightly golden. Don’t overcook—fish hates drama and rubbery textures.
Remove the fish to a plate. In the same pan, add shallot and garlic; sauté until fragrant and translucent, about 1–2 minutes.
Whisk in the mustards, lemon juice, and broth. Scrape up any tasty bits from the bottom. Simmer 2–3 minutes until the sauce thickens slightly.
Return the fish to the pan, spooning the sauce over it. Warm through for another minute so the flavors mingle without turning the fish into mush.
Taste and adjust with a pinch more salt, pepper, or lemon if you’re feeling feisty. Garnish with parsley or dill and serve.