Make the spiced coffee ice cubes: Combine the espresso, sugar, orange peel, cloves, cinnamon sticks and ginger in a medium bowl until the sugar dissolves. Cool to room temperature, and then cover with plastic wrap and refrigerate for at least 4 hours and up to 24 hours. Strain the coffee mixture through a fine-mesh sieve set over a large bowl and discard the solids. Divide the mixture among 2 ice cube trays and freeze until solid, at least 2 hours.
Make the lassi: Add 3/4 cup orange juice, the yogurt, banana and cocoa powder to a blender and puree until smooth (if you'd like the lassi to be a bit thinner, blend in the remaining 1/4 cup orange juice). Add a few spiced ice cubes to the blender and puree. Pour the lassi into glasses and add 2 more spiced ice cubes to each glass. Serve immediately.