Add the piquillo peppers to a food processor and puree.
In a stand mixer, combine the cream cheese, smoked Gouda and piquillo peppers. Taste and season. If the mixture feels too loose to mold, refrigerate for 30 minutes.
Roll the mixture into 2 balls. Divide the bunch of parsley into 2 parts and place on separate serving plates. Place each cheese ball on top of the parsley sprigs so that the parsley looks like carrot stems. Shape each ball of cheese into a carrot shape and top with some of the Cheddar, pushing the cheese in slightly so it stays.
Refrigerate or serve immediately with crudite or chips.