This recipe teaches the classic French technique of pan-searing fish to achieve a crispy exterior while maintaining a moist, tender interior. The accompanying white wine sauce demonstrates fundamental sauce-making skills that can be applied to many other dishes.

1. Step 1: Thoroughly drying the fish is crucial for achieving a good sear.

   Pat the fish fillets dry with paper towels. Season both sides with 3/4 teaspoon salt and black pepper. Lightly dust with flour, shaking off any excess.

2. Step 2: The pan should be hot enough that the fish sizzles when it touches the surface.

   Heat a large non-stick or cast-iron skillet over medium-high heat. Add the oil and 1 tablespoon of butter. When the butter stops foaming, carefully add the fish fillets, skin-side down if using skin-on fillets.

3. Step 3: Cooking time varies based on thickness - adjust accordingly.

   Cook without moving for 3-4 minutes until the bottom is golden brown and crisp. Gently flip the fillets and cook for another 2-3 minutes until the fish is opaque and flakes easily with a fork. The internal temperature should reach 145°F (63°C).

4. Step 4: Don't cover tightly or the steam will make the crispy exterior soggy.

   Transfer the fish to a warm plate and tent loosely with foil to keep warm.

5. Step 5: The shallots provide a sweet, aromatic base for the sauce.

   Reduce heat to medium and add the minced shallot to the same pan. Cook for 1-2 minutes until softened but not browned, stirring occasionally.

6. Step 6: These browned bits (fond) contain concentrated flavor that enriches the sauce.

   Add the white wine and increase heat to medium-high. Scrape up any browned bits from the bottom of the pan with a wooden spoon. Let the wine reduce by half, about 2-3 minutes.

7. Step 7: Reduction concentrates flavors and creates a more luxurious sauce.

   Add the chicken broth, lemon juice, and thyme. Continue to simmer until the liquid is reduced by half again, about 2-3 minutes.

8. Step 8: This technique of finishing with cold butter (mounting) creates a silky, glossy sauce.

   Reduce heat to low and whisk in the remaining 2 tablespoons of butter, one tablespoon at a time, until the sauce is smooth and slightly thickened. Stir in capers if using. Season with the remaining 1/4 teaspoon salt, adjusting to taste.

9. Step 9: The bright herbs and lemon add freshness that balances the rich sauce.

   Return the fish to the pan to warm briefly in the sauce, or plate the fish and spoon the sauce over each fillet. Garnish with chopped parsley, thyme sprigs, and serve with lemon wedges.

For best results, choose fresh, high-quality fish fillets of even thickness. If using frozen fish, thaw completely and pat very dry before cooking. The sauce can be customized by adding different herbs like tarragon or dill, or by incorporating a splash of heavy cream at the end for a richer variation.