Preheat the oven to 400°F., with a rack at the center of the oven. Butter a shallow baking pan or ovenproof skillet that will hold the fish in a single layer. Scatter the chopped shallots in the bottom of the pan. Season the fillets with salt and pepper to taste; carefully arrange them, without crowding, in the pan. Thick fillets can be placed in the pan as is, making sure the fit is not too snug; fold thinner fillets over, with skin (smooth) side inward and the thinner part on top. Pour enough of the wine around the fish to reach about halfway up it; add enough cold water so that the level of the liquids reaches not quite to the top of the fish. Cover with a buttered sheet of parchment or wax paper, buttered side down (this helps keep the fish moist).
Place the pan on a stove-top burner over medium heat. Bring the liquid just to a boil, watching carefully. The moment it begins to boil, carefully transfer the pan to the oven. Oven poach until the fish is just cooked—what you’re looking for is the center of the fillet to turn from translucent to opaque. This can take as little as 3 minutes for thin flounder fillets or up to 10 minutes for thicker fillets. Don’t overcook.
With a slotted spatula, lift the fillets from the broth, draining all possible broth back into the pan. (Reserve the poaching liquid for fish soups and stews.) Serve the fish as is, with or without a sauce, garnished with the watercress and lemon. Or cool it in its broth; remove and serve cold with an herbed mayonnaise.