Preheat oven to 400°F degrees.
In a saucepan, combine the milk, water, butter and a generous pinch of salt. Bring to a simmer over medium heat, allowing the butter to melt completely. Combine the cayenne and the flour and add to the milk mixture all at once. Cook, stirring with your Heat Resistant Spatula, until the paste pulls away from the pan, about 2 minutes. Continue stirring for another 2 minutes to allow the moisture to evaporate.
Off of the heat, add the mashed potatoes to the saucepan and combine. Return to the heat and stir for one minute. Taste and adjust the seasoning with salt and pepper.
Remove from the heat and while stirring, add the eggs. Continue stirring until a smooth batter is formed. Stir in the Parmesan cheese.
Transfer the mixture to your Pastry Bag fitted with the large open star tip. Pipe 2 inch-long dollops onto a large Bonmat placed on a Large Perforated Baking Sheet. Using your Silicone Pastry Brush gently brush each Puppy with melted butter.
Bake for 15 to 20 minutes until golden brown on top.
Remove from oven and sprinkle with salt or more Parmesan cheese, if desired. These are best served warm. You can make them ahead, when cool, store in refrigerator in airtight container and reheat on your Bonmat when ready to serve.