Rinse beef and pat dry; cut across the grain into 1/8-inch-thick slices and place in a bowl. In a blender, cover dried chilies with 3/4 cup boiling water; let stand until chilies are soft, about 15 minutes. Add lime juice, garlic, cayenne, and 1/2 teaspoon salt and whirl until smooth. Pour over beef, cover, and chill for 30 minutes.
In a 3- to 4-quart pan over high heat, bring 4 cups water and the brown rice to a boil. Cover, reduce heat to low, and simmer until liquid is absorbed and rice is tender to bite, about 45 minutes.
Meanwhile, pour oil into a 10- to 12-inch frying pan over high heat. When the oil is hot, lift beef from marinade with a slotted spoon (reserve marinade) and add to pan. Stir until meat is no longer pink, about 3 minutes. Transfer beef to a rimmed plate or bowl. Add peppers and onion to pan; stir frequently until limp, 5 to 6 minutes. Return beef to pan along with reserved marinade; bring to a boil and cook, stirring once or twice, for 1 minute.
Spoon rice into four wide, shallow bowls and top equally with beef, vegetables, and sauce. Sprinkle with cilantro. Add more salt to taste.