Combine cornmeal and salt: Preheat oven to 350°F. Whisk together cornmeal and salt in a large heatproof bowl.
Make batter, and shape patties: Using a rubber spatula, stir in boiling water and ¼ cup of the melted butter, stirring continuously until a smooth, thick batter forms, about 1 minute. Scoop 6 (¼-cup) portions of batter onto a large plate; mold each into a (2 ½- to 3-inch) patty, about ½-inch thick.
Fry patties: Melt remaining 2 tablespoons butter in a large cast-iron skillet over medium-high. Add patties, and cook until lightly browned and crisp, 3 to 4 minutes per side.
Finish baking patties: Transfer to a baking sheet, and bake in preheated oven until golden brown in spots, about 5 minutes. Remove from oven, and serve warm with salted butter.
