Place the milk, sugar, cloves, vanilla, cinnamon, lemon, and orange peels in a large pot. Bring to a soft boil over medium heat. When the milk begins to boil, add the instant coffee, dissolved in some warm milk. Stir to mix and turn off the heat and allow to cool covered. Strain into a bowl or pitcher. Add the pisco little by little, while stirring with a wooden spoon. Store in glass bottles and refrigerate.
Traditionally, cola de mono is prepared the day before it is to be served.