Set slow cooker to high. Heat ½ a tablespoon of vegetable oil in a large skillet over high heat. Add the squash and season with salt and pepper. Cook for about three minutes, turning occasionally until browned in spots. Transfer to the slow cooker.
Add another ½ tablespoon of vegetable oil to the skillet and add the onion and poblano. Season with salt and pepper. Cook for five to six minutes, stirring occasionally, until lightly browned. Scrape mixture into the slow cooker.
Warm 2 tablespoons of oil in the skillet. Add the turkey and cook on high heat for about five minutes, stirring occasionally, until lightly browned. Stir in garlic, chili powder, cumin, and chopped tortillas, and cook, stirring for one minute. Add one cup of the broth and scrape the bottom of the skillet to loosen any stuck pieces.
Place the turkey mixture into the slow cooker and stir in the remaining broth. Season with salt and pepper. Cover and cook on high for four hours or on low for eight hours.
Serve over brown rice and top with avocado, cilantro, and sour cream.