Combine milk and eggs in a blender; pulse until well mixed. Add flour, cocoa powder, sugar, baking powder, and salt; pulse until batter is well blended. Add water 1 tablespoon at a time if batter appears too thick.
Heat a lightly oiled griddle over medium-high heat. Drop 1/3 cup batter onto the griddle and cook until bubbles form and the edges are dry, 2 to 3 minutes. Flip and cook until browned on the other side, 2 to 3 minutes. Repeat with remaining batter until you have at least 6 pancakes. Transfer pancakes to a wire rack to cool.
Mix cherry puree and vodka together in a bowl.
Brush 1 pancake with cherry puree mixture and pipe whipped cream on the edge of the pancake; top with another pancake. Repeat until all the pancakes, cherry puree mixture, and whipped cream are used. Top with sweet cherries and chocolate shavings. Cut cake using a serrated knife.