Mix the cake mix with the espresso powder in a large bowl. Prepare and bake the cake according to the package directions for a 9-by-13-inch baking dish. Cool completely on a wire rack. Use the handle of a wood spoon to poke 25 holes in the cake (make 5 rows of 5).
Meanwhile, whisk the sweetened condensed milk, pudding mix, milk and cardamom in a large bowl until smooth. Set aside at room temperature until ready to use.
Whip the heavy cream and vanilla in a large bowl with an electric mixer on medium speed until stiff peaks form, about 3 minutes.
Fill each hole with some of the pudding mixture and spread the remaining on top. Push an espresso bean into each hole. Spread the whipped cream on top. Using an offset spatula, create swirls. Dust the cake with the cinnamon and sprinkle with the chopped espresso beans. Chill for at least 1 hour and up to 6 hours. Serve cold.
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