Season both sides of the flounder fillets evenly with salt. Let stand at room temperature for 5 minutes while you preheat the oven to 450 degrees F. This brief rest takes some of the chill off the fish and gives the salt time to season the delicate flesh.
Line a rimmed baking sheet with parchment paper. Arrange the fillets in a single layer, leaving a little space between them so they roast rather than steam. Brush the tops evenly with the olive oil.
Cut the butter into 8 equal pieces and place one piece in the center of each fillet. As the fish bakes, the butter will melt across the surface and mingle with the olive oil, keeping these lean, thin fillets moist while adding richness.
Bake until the butter has melted and the flounder is opaque and flakes easily when gently pressed with a fork, about 5 minutes. Because flounder fillets are thin, begin checking at 4 minutes. The flesh should have lost its translucent appearance but still look moist; another minute can be the difference between tender fish and dry fish.
Remove from the oven and season with freshly ground black pepper. Spoon any melted butter and juices from the baking sheet over the fillets and serve two fillets per person immediately with your favorite sides.