Bring Irish stout beer and 1 cup butter to a boil in a saucepan and set aside until butter has melted, stirring occasionally. Mix in cocoa powder until smooth.
Whisk together flour, sugar, baking soda, and salt in a bowl until thoroughly combined.
Beat eggs with sour cream in a large bowl with an electric mixer on low until well combined. Slowly beat in the beer mixture, then the flour mixture; beat until the batter is smooth.
Divide batter between the prepared cupcake cups, filling each cup about 2/3 full.
Bake in the preheated oven until a toothpick inserted into the center of a cupcake comes out clean, about 17 minutes.
Cool the cupcakes completely. Cut cores out of the center of each cupcake with a sharp paring knife. Discard cores.
Bring cream to a simmer in a saucepan over low heat; stir in bittersweet chocolate until melted.
Mix in 2 tablespoons butter and Irish whiskey until butter is melted; let mixture cool to room temperature. Filling will thicken as it cools.
Spoon the filling into the cored cupcakes.
For frosting, whip 1/2 cup butter in a bowl with an electric mixer until fluffy, 2 to 3 minutes.
Set mixer to low speed and slowly beat in confectioners' sugar, 1 cup at a time, until frosting is smooth and spreadable. Beat in the Irish cream liqueur; adjust thickness of frosting with more confectioners' sugar if needed.