Combine the spices in a medium bowl, then add the chicken. Cover and store in the refrigerator until you’re ready to use.
Pierce sweet potatoes with a fork and microwave on high until almost tender when pierced with a knife, about 2 minutes. Cool completely. Halve lengthwise, then slice each half diagonally into 1/2-inch-thick pieces.
Heat 2 teaspoons oil in a large skillet over medium heat. Add chiles and saute until softened slightly, about 8 minutes. Add onion and sweet potatoes and saute, only stir once or twice, until they begin to brown (I like them to get a little charred), about 8 minutes; transfer vegetables to a large bowl.
Heat remaining oil in the same skillet. Add the spiced chicken and saute until it is browned and cooked through, about 6 minutes. Return vegetables to skillet; add garlic and broth and simmer until liquid is almost evaporated, about 2 minutes.
Place warm tortillas on a plate, sprinkle with cheese, then top with the fajita mixture. Garnish with a few cilantro leaves.