In a blender, cover chilies with 3/4 cup boiling water. Let stand until softened, about 15 minutes.
Meanwhile, rinse beef and pat dry. Cut across the grain into 1/8 inch thick slices and place in a non-reactive bowl (such as glass).
Add lime juice, garlic, cayenne, and 1/2 tsp salt to soaked chilies. Blend until smooth. Pour over beef strips, cover, and chill for 30 minutes.
Meanwhile, in a 3-4 quart pan over high heat, bring 4 cups water and the rice to a boil. Cover, reduce heat, and simmer until liquid is absorbed and rice is tender to bite, about 45 minutes.
After beef has marinated and while rice cooks, heat olive oil in a 10-12 inch skillet over high heat. Lift beef out of marinade with a slotted spoon, reserving marinade, and add to pan. Stir-fry until no longer pink, about 3 minutes. Transfer to a bowl.
Add peppers and onions to pan. Stir-fry until limip, about 5-6 minutes. Return beef to pan along with reserved marinade. Bring to a boil; cook, stirring 1-2 times, for 1 minute.
Spoon rice into four wide, shallow bowls. Top with equal portions of beef mixture and sauce. Sprinkle with cilantro, and season to taste with salt.