In a small bowl, combine cumin, garlic powder, smoked paprika, onion powder, salt, black pepper, and cayenne (if using). Stir until evenly blended.
Pat chicken breasts completely dry with paper towels. If very thick (more than 1 inch), pound to even thickness. Drizzle with olive oil and sprinkle spice blend generously over both sides, pressing gently to adhere.
Heat cast iron skillet over medium-high heat for 2 minutes. Add olive oil and swirl to coat. Place chicken in pan and cook undisturbed for 5-6 minutes until golden brown and releases naturally. Flip and cook other side 5-6 minutes more.
Check internal temperature in thickest part with instant-read thermometer. Chicken is done at 165°F (74°C). Transfer to a plate and let rest for 5 minutes before slicing.
While chicken cooks, dice mangoes. Slice each mango lengthwise on either side of the flat seed. Score each half in a crosshatch pattern without cutting through skin, then invert and slice cubes into a mixing bowl.
Add red bell pepper, red onion, jalapeño, and fresh cilantro to the bowl with mango. Pour in lime juice and season with salt and pepper. Stir gently to combine without turning mushy. Taste and adjust seasoning.
Slice rested chicken against the grain into 1/2-inch thick slices. Arrange on a serving platter or individual plates. Spoon mango salsa generously over the top. Garnish with cilantro sprigs and lime wedges, and serve immediately.