In a deep frying pan, sauté pan, or wide pot over medium-high heat, melt 2 tablespoons of the butter or heat the oil. Add the garlic and red pepper flakes, if using. Cook, stirring, until just barely turning golden, about 2 minutes. Add the greens, with whatever water is still clinging to their leaves, and sprinkle them with half of the salt. Stir or toss the greens until they start to wilt, about 1 minute.
Add the broth, wine, or water, cover, and cook until the greens are tender, about 10 minutes.
Remove the lid and stir the greens. There should be just a bit of liquid in the bottom of the pan; if not, add 2 tablespoons of water.
Set the fish on the greens. Sprinkle the fish with the remaining salt, as well as black pepper to taste. Dot the tops of the fillets with the remaining butter or drizzle with the remaining oil. Cover and cook until the fish is cooked through; 10 minutes per inch of thickness should do it.
Transfer to plates or shallow bowls and serve with wedges of lemon for spritzing.