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1. Place a rack in the center of your oven and preheat to 425°F (220°C).
2. In a large, shallow plate (a pie dish works well), combine the flour, 1 teaspoon salt, and pepper.
3. Pat the salmon fillets dry with paper towels and sprinkle the remaining ¼ teaspoon salt over the top.
4. Melt the butter in a large (12-inch) oven safe cast iron skillet or similar sturdy-bottomed oven safe skillet over medium heat.
5. Continue to heat, swirling the pan periodically, until it begins to brown.
6. Reduce the heat to medium-low.
7. Dredge both sides of the salmon fillets in the flour mixture.
8. Shake off the excess then gently place them in the hot butter, top-side down.
9. Cook without disturbing them for 3 minutes, until the top is golden brown.
10. When the salmon turns opaque on the sides and starts to turn opaque on top, use a flexible spatula to flip the salmon.
11. Add the lemon zest and lemon juice to the pan.
12. Place the skillet immediately into the oven and let cook for 6 minutes (the salmon will appear a little undercooked in the center but will finish cooking as it rests).
13. Remove from the oven and cover with foil.
14. Let rest 4 to 5 minutes.
15. To serve, place each piece of salmon on a plate and spoon the pan sauce liberally over the top.
16. Sprinkle with fresh parsley and capers.
17. Season with additional salt and pepper to taste.
18. Enjoy immediately.

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