Combine all ingredients for the spice mix in a small bowl; divide in half.
Mix together the chicken, yogurt, lemon juice, cracked garlic cloves, ½ the spice mixture, and ¼ teaspoon salt in a medium bowl; cover and refrigerate 2 to 24 hours, stirring occasionally.
Heat the oil in a large pot over medium heat; add the onion, green bell pepper, and red bell pepper. Cook until the vegetables are starting to soften, about 5 minutes, stirring occasionally. Add the garlic, ginger, bay leaf, remaining ½ of the spice mixture, and remaining 1 teaspoon salt, and cook 1 minute more, stirring constantly. Stir in the tomato puree, chicken stock, and tomato paste; bring the soup up to a boil, then turn heat down and simmer (uncovered) until the vegetables are tender, about 15 minutes, stirring occasionally.
Cook the chicken while the soup simmers. Preheat oven to 450F. Remove any excess marinade, and spread the chicken out on a large baking sheet that has been sprayed with nonstick spray. Bake until the chicken is fully cooked, about 10 to 12 minutes, flipping once halfway through. (The chicken is done when there is no pink inside.)
Remove the bay leaf from the soup, and puree using an immersion blender or in batches using a regular blender. Pour the soup back into the pot and reheat as necessary; turn off the heat and add the cream and cooked chicken. (Once the cream is added, don't let it come back up to a boil.)
Taste and add salt, pepper, hot sauce, and/or honey to taste.
To serve, pour into individual bowls, sprinkle on the cilantro or parsley (if using), and serve along with fresh lemon wedges to squeeze into the soup if desired.
Notes
Net Carbs: 17g per serving (⅙ of recipe)Paleo/Whole30 Version: For the chicken marinade, omit the yogurt and increase the lemon juice to 2 tablespoons. Finish the soup with full-fat coconut milk instead of cream. Skip the Naan and serve with Cauliflower Rice instead.Low Carb Version: Skip the Naan and serve with Cauliflower Rice instead.