Red and green chile are two manifestations of the same pepper that together form the backbone of New Mexican cuisine. Both colors, and their accompanying, exceptional flavors, are worth discussion and praise.
But red was the original chile, the chile that has fed this region year-round for centuries. The pods are harvested after turning a deep shade of red, and sun-dried. Red chilies are often stored decoratively in beautifully strung ristras, though for practical purposes, storing red chili in powder form makes the most sense. And because red chili is low-maintenance and cheap to transport and store, it's ubiquitous in the U.S.
Red chile is a forgiving dish, with plenty of room for error and creativity. At the very least, it is nothing but oil, water, chili powder, and salt. But onions, garlic, butter, chicken stock, oregano, and pumpkin seeds really help. I use a clean coffee grinder for the seeds, which gets them to a peanut butter-like consistency.
Even if you like spicy food, I recommend using the mildest red chile you can get. Too much heat can make it hard to taste the sweet, acrid flavor of the chile. If you require a certain level of heat, keep some hot chili powder available.
For a quart of basic red chile sauce, start with two tablespoons oil and a tablespoon of butter in a pan on low/medium. When the oil is hot, add a medium onion, minced. A clove of garlic can also be grated in at this point. Cook slowly until the onion sweats and caramelizes. Remove the pan from heat and stir in a tablespoon of ground pumpkin seeds, a tablespoon of oregano, and a sprinkling of garlic salt. Then add one cup of mild red chili powder, and mix it thoroughly with the other ingredients.
Add three cups of water or stock (or a combination of the two), a cup at a time, stirring carefully to hydrate everything. You want the chile about the consistency of a coconut curry or turkey gravy. Add more water if necessary, a little at a time, until it thickens properly. Return briefly to the heat until it reaches a simmer. If you added too much water you can cook it further in order to thicken it, but it will darken and can get more bitter with prolonged cooking.
There are two basic ways of using red chile. One is as a condiment, served with scrambled eggs, a hamburger, fries, fish ... anything savory.
Alternatively, red chile can be used as an ingredient, added to liven and redden something else, or as the medium in which things are cooked. Chopped meat simmered in red chile is called carne adovada. Shrimp simmered in a chile-and-tomato red sauce is the Mexican dish Camarones Diablo, or devil shrimp. You can simmer beans in red chile, or use it as a base for stew. But cook the beans or stew first, and then add the red chile at the end and simmer briefly.
The Spanish verb enchilar means to coat with chile, and I would be remiss not to mention the most famous conjugation of that word, enchilladas, the lasagna of the Southwest. Corn tortillas are covered in chile — enchiladan, as it were — and these lathered tortillas are layered, along with cheese and/or meat, and baked at 300 until warm and delicious.
Last but not least, a little red chile in chocolate cake, brownies, or pots de crème will add gravitas, without taking these desserts out of the realm of sweetness.