Add the oil to a large heavy pot over medium heat and allow it to warm up a bit. Add the garlic, poblanos, onions and bell peppers and season with a small pinch of salt and pepper. Saute until the veggies begin to cook down a bit and develop some color, 5 to 6 minutes.
Add the beer and deglaze the pot, scraping up any browned bits on the bottom. Add the tomato paste along with the chile powder, brown sugar, cumin and oregano and cook all together for about 1 minute, stirring the whole time.
Stir in the stock, diced tomatoes, black beans and green chilies. Bring to a simmer, turn the heat down to medium low and simmer for 45 minutes.
Add the squash and continue to simmer until the squash is tender when pierced with a fork but not mushy, about 30 minutes.
Season with salt and pepper to taste and serve with a dollop of cool sour cream and some fresh chopped cilantro, scallions and lime wedges.