Cut 4 tablespoons unsalted butter into 4 pieces and place in a medium microwave-safe bowl. Microwave until melted, 40 to 50 seconds. (Alternatively, melt in a small saucepan over medium heat, then transfer to a medium bowl.) Add 1 1/2 cups buttermilk, 1 cup pumpkin purée, 2 large eggs, 1/3 cup packed brown sugar, and 1 1/2 teaspoons kosher salt, and whisk until the sugar and salt are dissolved.