First, remove the stems from the dried chilis and as many seeds as possible. Next, place dried chilis in a bowl with hot water, submerging the chilis with a plate if needed until soft, about 15 minutes. Then, transfer the chiles and 1 cup of the soaking liquid to a high-powered blender along with the garlic. Puree until smooth.
Next, in a stock-pot or dutch oven, heat the olive oil over medium heat. Add the onion and poblano pepper and cook until brown, very soft and tender, about 15 minutes.
Then, add in the spices (chile powder, cumin, dried oregano, paprika) and cook another minute or two.
Then, stir in 1 cup of the chile sauce (can add more depending on spice preference), hominy, beans, vegetable broth, bay leaf and bring to a boil.
Next, reduce heat to low, cover and simmer for 20 minutes, until thickened.
Finally, stir in the lime juice and cilantro and season to taste as needed, with salt and pepper.