Melt the milk couverture in the oven at 88° to 90°F/31.1° to 32.2°C, or use tempered couverture.
In a bowl, blend the butter by hand with a spatula until smooth.
Mix the butter and couverture together by hand using a spatula or a stand mixer fitted with the paddle attachment. The closer the temperatures of the butter and the couverture, the easier it will be to blend them together. Stir to a smooth consistency.
Add the Cognac. Blend in the Cognac very well, by hand, using a spatula, or stand mixer to create a smooth ganache.
Pipe the ganache onto the chocolate discs using a pastry bag with a plain size-12 tip. If the ganache is too soft, let it set before piping. If the ganache is too cold, it can be warmed in a water bath or stirred. Stirring will aerate the ganache, leaving a lighter mouthfeel.
Let the piped ganache set for 1 hour at room temperature.
Once the ganache is fully crystallized, dip the pieces in the dark couverture using a dipping fork. Let the couverture completely set.
Store in an airtight container at 57° to 61°F/13.9° to 16.1°C in a dark, dry place.