Remove the stems and seeds from the chile pods. In a stockpot, cover the pods with water and simmer for a half hour to soften or just soak in warm water for a few hours. Once soft, drain and place the pods along with the garlic in a blender and puree—adding small amounts of fresh water if necessary—until a thick paste is formed.
Pass the paste through a food mill using the smallest grid to separate out the fibrous, bitter skins. This method should yield about 1 cup of bright red, very smooth chile paste.
Heat the oil in a stockpot over medium heat, slowly add the flour and whisk to make a roux. Add the chile paste to the roux and mix, then slowly add fresh water to create a sauce (for a thick sauce, add about 3 cups of water; for a thinner sauce, add about 4). Let the sauce cook down about 20 minutes.
Soften the tortillas either by steaming them or cooking each briefly in oil. (Don’t fry too long or you’ll have crunchy tortillas.) Serve individual plates of 3 enchiladas by layering each tortilla with sauce, cheese and onions and stacking (as is traditional in New Mexico). Serve with a generous amount of cheese on top.