In a large Dutch Oven heat 2 tablespoon of olive oil. Add onion, garlic and both types of peppers and cook over medium heat stirring occasionally for 10 minutes.
In a medium sauté pan heat the remaining 2 tablespoons of olive oil and add ground turkey thighs and breast. Cook, stirring constantly and breaking up the big chunks with a fork until the liquid evaporates and meat is thoroughly cooked and slightly brown, about 7-10 minutes.
Add cooked meat into a pot with an onion and pepper mixture.
Pour in diced tomatoes and beans.
Dilute tomato paste with 1 cup of chicken broth and add into a pot.
Add chili powder, cayenne pepper, smoked paprika, oregano, cumin, brown sugar, cocoa powder, the remaining chicken broth and ½ teaspoon of salt.
Give everything a good stir, cover with a lid and reduce the heat to low. If the soup becomes too thick, add ½ cup of chicken broth.
Simmer for 1 hour.
Adjust the seasoning and serve immediately with shredded Cheddar cheese and a dollop of sour cream.