Bake the chocolate cake as per the package instructions, using milk instead of water. Let it cool completely, then crumble into bite-sized pieces.
Beat softened cream cheese until smooth. Add powdered sugar and vanilla extract, then mix until fully combined.
Whip the heavy cream until stiff peaks form, ensuring it's thick but smooth. Avoid overwhipping.
Gently fold the whipped cream into the cream cheese mixture, using a spatula to maintain a light, fluffy texture.
Layer crumbled chocolate cake at the bottom of a trifle dish, drizzle with Baileys Irish Cream. Add a layer of cream cheese mixture, followed by chocolate chips. Repeat layers, finishing with cream cheese mixture on top.
Top with whipped cream, chocolate shavings, and chocolate chips. Refrigerate for at least 1 hour before serving.