In a small bowl, combine all of the spice mixture and set aside.
Heat a dutch oven or large pot over medium heat with olive oil. Add the yellow onion, red bell pepper, and green bell pepper. Saute, stirring until the vegetables are tender, about 5 minutes. While sautéing, season the vegetables with salt and pepper.
Once the veggies are tender, melt the ghee. Sprinkle in the arrowroot flour and stir until well combined. Add the spice mixture and the tomato paste and stir to combine. It's going to look a little bit messy/clumpy, but just bear with me.
While stirring, slowly pour in chicken broth, using a spoon to scrape up the brown bits on the bottom of the pot.
Add the diced tomatoes and green chile, stir to combine, and increase heat to bring to a boil.
Once boiling, reduce the heat and stir in the shredded chicken. Cook, simmering and uncovered, for 10 minutes, stirring occasionally.
Remove from heat, taste, and add more salt, if desired.
Ladle soup into bowls and top with the radishes, iceberg lettuce, and cilantro, and serve with lime wedges. Serve and enjoy!