Roast the poblano and jalapeño chiles under the broiler until blackened, about 5 minutes per side. Place the chiles in a paper sack or plastic food-storage bag, close it tight, and let the chiles steam for 20 minutes. After the chiles have steamed, remove them from the bag and rub off the skin. Remove the stems and seeds from the chiles.
Cut ¼ of the poblano off from the pepper (about 2 tablespoons) and reserve it for the crema. Place the remainder of the poblano and the entire jalapeño in a blender jar. (To cut the poblano, I cut it in half, then cut one of the halves in another half.)
Meanwhile, heat the oil on medium-low heat in a medium pot. Add the onion and while occasionally stirring, cook until softened about 5 minutes. Stir in the garlic and cook for 30 more seconds. Turn off the heat.
Transfer the onion mixture to the blender. Pour the 2 cups of the broth into the pot and swirl it around to get any remaining bits. Pour the broth into the blender.
Add to the blender the pumpkin puree, cumin, thyme, sage, allspice, and salt. Blend everything until smooth.
Pour the pumpkin mix back into the pot and add the remaining cup of broth. Turn the heat to high (it may splatter, so be ready!) and when it starts to boil, turn the heat down to low and let the soup simmer uncovered, while stirring occasionally, for 30 minutes.
After the soup has simmered, stir in the lime juice then taste and adjust seasonings.
As the soup simmers, rinse out the blender. To make the poblano crema, add the remaining ¼ poblano chile, sour cream, buttermilk, lime juice, cilantro, cumin, and salt. Blend until smooth then taste and adjust seasonings.
Serve the soup warm topped with fried corn tortilla strips and drizzles of the poblano crema.