Turn the broiler on high, then line a large baking tray with foil. Remove the husks and stems from the tomatillos and wash them thoroughly. Cut them in half and place them cut side down on the foil, then char under the broiler until darkened, roughly 15-20 minutes. Remove from the tray and puree in a blender.
Pour 2 tablespoons of olive oil into a large, heavy-bottomed pot at medium high heat and heat until shimmering. Cook the ground turkey until it's no longer pink, roughly 5 minutes. Drain the meat and set aside. If using leftover turkey, shred or chop into bite size pieces.
Heat the other 2 tablespoons of oil in the pot over medium heat until shimmering, then cook the onion and carrot until soft while stirring, roughly 5 minutes. Add the garlic and cook until fragrant, roughly 30 seconds.
Add the spices to the aromatics and cook for 1 minute, stirring constantly. Add the tomato paste and cook over medium heat, stirring for 2 minutes.
Increase the heat to medium high, then slowly pour in ½ cup of chicken stock while scraping the bottom of the pot with a wooden turner. This step will build more flavor.
Add the green chilis, molasses, turkey, the pureed tomatillos, and the canned tomatoes. (The tomatillos will add flavor and help thicken the soup.) Stir with a large wooden spoon, then cover and bring to a boil, then reduce heat to medium low and simmer for 30 minutes.
Dump in the shelled edamame, corn, red kidney beans, and the chickpeas. Taste and adjust seasonings, if necessary. Cover and simmer for another 20 minutes.
Remove the soup from the heat and stir in the cilantro and freshly squeezed lime juice.
Garnish with grated pepper jack cheese, sour cream, tortilla strips, and chopped cilantro. Panera Bread serves their turkey chili plain with a side order of kettle chips, French baguette, or an apple. Leftovers can be stored in an airtight container in the fridge for up to 4 days.