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Preheat oven to 350 degrees. Spray a 9- by 5-inch loaf pan with cooking spray. Line with parchment paper, allowing a couple inches of excess to hang over the sides. Spray paper with cooking spray, then dust with flour. Tap out excess flour; set pan aside.
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Combine butter, sugar, cocoa powder, vanilla, espresso powder, salt, and baking powder in the bowl of a stand mixer fitted with the paddle attachment. Mix on medium speed until combined and smooth, about 30 seconds. Add the eggs one at a time, mixing well and scraping down the sides and bottom of the bowl after each addition.
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Turn the mixer to low and add half of the flour and mix until just incorporated. Add all of the milk, mixing until just incorporated, then add remaining flour. Mix on low until just incorporated.
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Pour just enough batter into the prepared pan to cover the bottom evenly. Remove funfetti bunnies from the freezer and line them up to form a bunny log that is a little shorter than your pan—you’ll probably have an extra bunny or two. Set log carefully on top of batter, then carefully pour remaining batter over them, to just under the rim of the pan. You’ll have excess batter; I recommend pouring it into a ramekin and baking yourself a cupcake. Bake bunny cake for 44 to 50 minutes, until a toothpick inserted into the center of the cake comes out clean.
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Cool in pan on a wire rack for 10 minutes, then use parchment paper to remove the cake from the pan. Cool completely on a wire rack. Serve, enjoy, and watch your friends’ faces light up when they see that little bunny hiding in their cake.