Make the port wine reduction: Add enough canola oil to a large nonreactive stockpot to cover the bottom and set it over high heat. Just before the oil starts smoking, add the shallots, mushrooms and peppercorns and reduce the heat to medium. Sweat the vegetables until brown bits form on the bottom of the pan, about 5 minutes, then add the sugar. Add the red wine and port and deglaze the pan, scraping the brown bits off the bottom. Simmer the liquid until it has reduced to about 1 1/2 cups, about 40 minutes. Add the stock and cook until the liquid has reduced to 1 1/2 cups, about 15 more minutes. Be sure to skim off any foam that forms on the surface.
Transfer the liquid to a heatproof bowl. Add the thyme and bay leaf, then cover tightly with plastic wrap. Let infuse 1 hour. Strain through a fine-mesh strainer into a saucepan and set aside.
Make the steaks: Position racks in the upper and lower thirds of the oven; preheat to 350 degrees F. Thoroughly blot the meat dry and season both sides liberally with salt and pepper. Add enough canola oil to 2 large skillets to cover the bottoms (about 2 tablespoons each) and set over high heat. Just before the oil starts smoking, add a steak to each skillet and cook 6 minutes. Check the bottoms of the steaks to see if they are charred to your liking. Flip the steaks with tongs and add 1 tablespoon butter to each skillet. Cook, tilting the skillets and spooning the butter over the steaks, 2 more minutes.
Transfer the steaks to a rimmed baking sheet; transfer to the oven and bake until a meat thermometer registers 125 degrees F (medium rare), an additional 3 minutes. Transfer the steaks to a cutting board and let rest at least 7 minutes before serving.
Meanwhile, warm the port wine reduction until it simmers. Stir in the berries and cook 30 seconds. Remove from the heat.
Slice the steak off the bone in 1 piece with a sharp knife, then slice the meat against the grain. Serve with the port wine reduction and crumbled blue cheese.