Preheat the oven to 350°F

Season the short ribs with salt and pepper.

Heat a large roasting pan with a lid over medium-high heat and pour in the canola oil. Add the ribs and sear on all sides until well browned. Transfer to a plate.

Add the peppers, onions, celery and garlic and cook, stirring occasionally, until caramelized. Add the wine and deglaze, stirring to scrape up the browned bits from the bottom of the pan. Add the stock and tomato sauce and bring to a boil.

Return the ribs to the pan, cover with the lid and transfer to the oven. Cook until the meat is tender when pierced with a fork, 2 to 2 1/2 hours.

Transfer the ribs to a platter and cover with aluminum foil. Skim the fat off the sauce. Strain the sauce through a fine-mesh sieve and discard the solids. Season the sauce with salt and pepper.

In a saucepan over medium-high heat, combine the stock and mushroom stems and bring to a simmer. Cook for 5 minutes, then puree in a blender. Set aside.

Heat a large sauté pan over medium heat and pour in the olive oil. Add the onions, thyme and sage and cook, stirring occasionally, until the onions are translucent. Add the mushrooms and cook, stirring occasionally, until softened.

Add the barley and stir to combine with the onion-mushroom mixture. Add the sherry and cook, stirring with a wooden spoon. Add the stock 1 cup at at time while continuing to stir and cook until the barley is tender. Season with salt and pepper.

Serve the short ribs over the barley-mushroom risotto.