Heat oil in Dutch oven over medium-high heat.
Add lamb and cook, breaking up with a wooden spoon until well browned, approximately 5 minutes. Season with salt, pepper, and smoked paprika. Transfer lamb to a paper towel covered plate.
Add onion, poblano peppers, and jalapeño peppers to Dutch oven. Cook for until softened, approximately 5 to7 minutes.
Add 2 tbsp of cilantro stems and garlic. Cook until both have released fragrance, approximately 2 minutes.
Add all spices to the Dutch oven and cook for 1 minute to bloom. Stir in tomato paste and cook until it begins to brown.
Return lamb to the Dutch oven. Add stock, water, Gaya cilantro soup base, kidney beans, and tomatoes. Salt to taste. Bring to a boil then reduce temperature to simmer at low heat for 45 minutes, stirring occasionally. Add more water if the chili becomes too thick.
Add 1 tbsp of lime juice and stir. Adjust seasonings if necessary.
Serve with shredded pepper jack cheese, roughly chopped cilantro leaves, minced red onion, and lime wedges.