Cook is a verb. They are not actually cooking the recipe. They are using the recipe as an instruction guide. The recipe tells them what to cook, or how to cook it.

Tiffany, there are three uses for the different forms of the word 'cook' in your scenario. (1) In addition to exciting tours and lavish hotels, some travel agents will offer their clients the option to take cooking classes in exotic locations, such as the opportunity to learn how to make pasta from scratch with an authentic Italian Nona (grandmother) in Rome. In this scenario, the word 'cooking' functions as an adjective modifying the word 'class'. [Technically, it is a gerund acting as an adjective, but since that's pretty advanced grammar, we can just call it an adjective to keep things simple for our purposes here.] (2) When you get to the destination, Nona Maria will welcome you then demonstrate how to make her famous pasta dish from scratch. One of her steps will be to simmer the sauce in a pan and boil the pasta in water, to cook the food before cheerfully offering you a taste. Here, 'cook' is a verb. The verb usually has a direct object, like in this case, cook the pasta in boiling water and the meat in the sauce by simmering it in the pan, but the object can be a little more abstract, like when someone says that they will 'cook dinner'. Dinner is meal consisting of several items, so in that sense, "dinner" acts as stand-in to describe the act of preparing several dishes through some kind of cooking method. (3) Getting back to our cooking class, after demonstrating the technique, Nona Maria will provide you with a written recipe or preparation instructions, as well as the materials to try to make the pasta dish yourself. Since you will be making your own pasta, at this point you would not only be a tourist, but also a student and a cook - the word 'cook' being a noun to describe describing the person who prepares the food. I hope this clears things up for you. Let us know if you have any other questions.