Cut sirloin into strips 2" long, ½" thick and ½" wide. Set them side.
Heat butter with 1 tablespoon of oil in a 5-quart Dutch oven over medium heat. Add the onion, shallot and dried red peppers; cook 1 minute. Add the garlic; cook 4 minutes longer. Using a slotted spoon, transfer the mixture to a plate.
Add 2 tablespoons of oil to the same pot. Sauté the mushrooms until golden, about 5 minutes. Using a slotted spoon, transfer them to the plate with the onions.
Add 2 more tablespoons of the oil to the same pot. Sauté the beef strips, _ at a time, over medium-high heat until browned on all sides. Transfer the beef to a separate plate.
Reduce heat to medium-low. Add the barley and rice, and stir well. Add the stock, scraping the sides and bottom of the pot with a wooden spoon. Add the reserved onion-mushroom mixture, and heat to boiling. Then reduce the heat and simmer, covered, over medium-low heat until the barley and rice are tender and almost all the liquid has been absorbed, about 35 minutes.