In a large bowl, using a whisk or hand mixer, beat the eggs, brown sugar, granulated sugar, melted butter, apple cider vinegar, vanilla, cinnamon, salt, and nutmeg together.
4 large eggs, 1 cup brown sugar, ½ cup granulated sugar, ½ cup unsalted butter, 2 tablespoons apple cider vinegar, 1 teaspoon pure vanilla extract, ½ teaspoon ground cinnamon, ½ teaspoon kosher salt, ⅛ teaspoon ground nutmeg