Preheat oven to 325 degrees Fahrenheit. Grease and flour a 12-cup Bundt pan and tap out the excess flour.

In a large saucepan over medium heat, melt two cups root beer, cocoa powder, chocolate, and margarine or butter until combined. Add granulated and dark brown sugars and whisk until dissolved.

Remove from the heat and let mixture cool. Whisk in eggs.

In a bowl, combine flour, baking soda, salt, and allspice. Gently fold flour mixture into root beer mixture (the batter will be slightly lumpy).

Pour batter into the prepared pan and bake until a toothpick inserted in the center comes out clean, 55–60 minutes, rotating the pan halfway through. Transfer to a cooling rack.

Gently poke the cake all over with a skewer and pour remaining 1/4 cup root beer over the cake. Let it cool in the pan for 20 minutes, then invert the cake onto a serving plate and let cool the rest of the way.

With an electric mixer, beat melted ice cream with margarine, powdered sugar, and vanilla. Add salt and beat until smooth. Drizzle glaze over the cake.