Place the chopped chocolate and softened butter in a medium heatproof bowl.
Heat the heavy cream in a small saucepan over medium-low heat until it just begins to simmer. Do not let it boil.
Pour the hot cream over the chocolate and butter. Let stand for 2 minutes, then gently stir until completely melted and smooth.
Stir in the Champagne until fully incorporated.
Cover and refrigerate for 2–3 hours, or until the chocolate mixture is firm enough to scoop.
Line a baking sheet or plate with parchment paper.
Using a small cookie scoop or teaspoon, portion the chocolate mixture and quickly roll each portion between your palms to form a ball.
Roll each truffle in Dutch-process cocoa powder until evenly coated.
Refrigerate until ready to serve. For the best texture, let the truffles sit at room temperature for about 10–15 minutes before serving.