Mix tomatoes, red onion, cilantro, jalapeno pepper, and juice of 1/2 lime together in a bowl. Cover and place in the refrigerator.

Combine 1 cup chicken broth and quinoa in a small pan. Bring to a boil. Reduce heat, cover, and simmer until chicken broth is absorbed, about 15 minutes. Remove from heat.

Heat olive oil in a large skillet over medium heat. Cook and stir sweet onion until softened, about 5 minutes. Add chicken; cook and stir until no longer pink, 6 to 8 minutes. Stir in cooked quinoa, remaining 1 cup chicken broth, black beans, prepared salsa, chili powder, and garlic. Simmer over low heat for 10 minutes.

Remove skillet from heat. Squeeze lime juice all over. Divide among serving bowls. Top each serving with homemade salsa and 1 avocado half. Season with salt and pepper.