Prepare and bake the brownie mix according to package directions in a 9x13 inch pan. Let cool completely, then cut into 1-inch cubes. You should have about 6 cups of brownie pieces.
In a large bowl, whisk together the instant chocolate pudding mix and cold milk for 2 minutes until thickened. Refrigerate for 5 minutes to set completely.
In a separate chilled bowl, beat the heavy cream with powdered sugar and vanilla on high speed until stiff peaks form, about 3-4 minutes. Do not overbeat or it will turn grainy.
To assemble, spread one-third of the brownie cubes in the bottom of a 3-quart trifle dish or clear glass bowl. Press some pieces against the sides for visual appeal.
Spread half of the chocolate pudding over the brownie layer, then dollop and spread half of the whipped cream on top. Sprinkle with 1/3 cup mini chocolate chips.
Repeat layering with another third of the brownies, remaining pudding, remaining whipped cream, and another 1/3 cup mini chips.
Top with the final third of brownie pieces arranged decoratively. Garnish with remaining mini chips and chocolate shavings or a dusting of cocoa powder.
Cover and refrigerate for at least 2 hours or up to 24 hours before serving. The layers will set and flavors will meld beautifully. Scoop generously to serve, making sure each portion includes all the layers.
