In a small bowl, combine the cumin, paprika, garlic powder, cinnamon, and ¼ teaspoon salt. Sprinkle the spice mixture over the chicken pieces, tossing well to coat.
In a large Dutch oven or pan, heat 1 tablespoon olive oil over medium heat. Add the chicken in one layer, being careful not to overcrowd the pan (you may need to sauté the chicken in 2 batches). Sauté for 4-5 minutes on the first side, or until golden brown. Flip the chicken and sauté an additional 4-5 minutes or until both sides are browned and crisp. Remove the chicken from the pan and set aside.
Add 1 teaspoon olive oil to the pan along with the nectarines, lemon juice, and honey (if using). Sauté over medium-low heat, scraping the browned bits from the bottom of the pan until the apricots are just softened, about 4 minutes. Remove the nectarine mixture from the pan and set aside.
Wipe the pan clean, then add 1 teaspoon olive oil and the zucchini. Sprinkle with ¼ teaspoon salt, then sauté over medium-high heat, flipping once, until browned and cooked through on both sides, about 8 minutes.
Assemble the final dish by arranging the cooked chicken, zucchini, green olives, and nectarine sauce in bowls. Sprinkle with chopped almonds and mint. Serve warm.