In a large Dutch oven, heat the avocado oil over medium heat. Once hot, add the onion, poblano, and jalapeño. Sauté, stirring occasionally, until the veggies soften, about 5 minutes.
Add in the garlic, chili powder, cumin, oregano, salt, and pepper. Stir to combine and cook until the spices are fragrant, about one minute.
Add in the chicken, breaking it up with the back of a wooden spoon. Cook until the chicken is fully cooked, stirring occasionally, about 6-8 minutes.
Pour in 1 can of the drained beans, 2 cups of the bone broth, and the green chiles. Stir to combine.
In a high-speed blender, add the remaining can of drained beans, 2 cups of bone broth, and pumpkin seeds. Blend until totally combined, about 30 seconds.
Pour the mixture into the Dutch oven and stir to combine. Bring the mixture up to a simmer. Once simmering, turn the heat down to low and continue to simmer uncovered for about 25-30 minutes, stirring intermittently. The liquid in the chili will reduce considerably during this time. Remove from the heat and add the lime juice and fresh cilantro.