Roast the chiles and peppers by the Open-Flame Method. Peel the chiles and peppers, pull off the stems, remove the seeds and veins, and set aside.
In a medium saucepan, parboil the potatoes in boiling water with 1 teaspoon of the salt until tender.
Puree the green chiles and then the red peppers separately in a food processor until smooth. Mix the purees together, add the potatoes and stock, and process in 2-cup batches for another minute, or until smooth. Add the remaining salt, the pepper, and garlic and process again. Press the puree through a fine sieve.
Heat the puree in a saucepan. Serve hot, garnished with tumbleweed greens.