Preheat your oven to 350 degrees Fahrenheit. Lightly grease a 9×9 inch square baking pan or line it with parchment paper, leaving an overhang on the sides for easy removal later.
In a large mixing bowl, combine the melted butter, granulated sugar, and 1/2 cup of cocoa powder. Whisk until smooth. Stir in the alcohol-free vanilla extract and the eggs one at a time, beating well after each addition until the batter is glossy.
Gently fold in the all-purpose flour and salt. Use a spatula to mix until just combined, being careful not to overmix the batter, as this can make the brownies tough instead of fudgy.
Pour the batter into the prepared pan and spread it evenly. Bake for 25 to 30 minutes, or until a toothpick inserted into the center comes out with just a few moist crumbs. Allow the brownies to cool completely in the pan before frosting.
In a medium bowl, beat the softened butter until creamy. Gradually add the powdered sugar, 1/3 cup cocoa powder, milk, and alcohol-free vanilla extract. Beat on medium-high speed until the frosting is light, fluffy, and spreadable.
Once the brownies are entirely cool, spread the chocolate frosting over the top in an even layer. Immediately garnish with red and green sprinkles or your favorite holiday decorations before the frosting sets. Cut into 16 squares and serve.