Mix the chili powder, cumin, salt and pepper in a medium bowl. Add the boneless skinless chicken breasts and toss to coat well. Heat the olive oil in a thick-bottomed sauté pan on medium high heat. Add the chicken breasts and cook for two minutes on each side. Lower the heat to low and cover the pan and cook until the breasts are just cooked through, about 4 to 5 more minutes. Remove the chicken from the pan and let cool to touch.
In the same pan that you used to cook the chicken, add the drained hominy. Toss with the remaining seasoning in the pan. Sprinkle with a little more salt, chili powder and ground cumin, to taste. Cook on medium high heat for 1 to 2 minutes. Remove from heat.
Whisk together the vinaigrette ingredients in a small bowl. Set aside.
Slice the cooled chicken across the grain of the meat in 1/4-inch thick slices. Peel and slice the avocado.
Toss the romaine lettuce, cabbage, green onion, cilantro, radish, and hominy with half of the vinaigrette. Arrange on chilled serving plates. Place several slices of chicken and avocado on top of each plate of greens. Sprinkle with cotija (or feta) cheese. Drizzle the remaining vinaigrette over the salads.