Stem and seed dried chilies. Place in small saucepot with stock, bring to boil then reduce heat to a low boil and simmer until peppers are tender and plump; purée.
Heat oil in a large pot over medium-high heat, 2 turns of the pan. Add onions and garlic, and cook to tender, 6-7 minutes. Stir in dried spices, cook 1 minute to toast then add beer. Reduce to 1/2 cup and add squash, black beans and chili purée. Bring chili to a bubble, reduce heat and simmer partially covered until squash is tender and chili is fairly thick.