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Step 1
Heat the oven to 475°F with a rack in the lower-middle position. In a small bowl, combine the porcini mushroom and boiling water; set aside. Meanwhile, in a large roasting pan, combine the pancetta, oil, cremini mushrooms, onions, carrots, celery, garlic and tomato paste. Using your hands, rub the paste into the other ingredients. Roast, without stirring, until deeply browned, about 40 minutes.
Step 2
While the aromatics are roasting, in a large saucepan over medium, bring the wine to a bare simmer, then reduce to medium-low to maintain a bare simmer (it should steam, with only a few bubbles occasionally breaking the surface), until reduced to about 1½ cups, about 30 minutes. Remove from the heat and add the broth, bay, thyme and rosemary. Using a fork, transfer the porcini from their soaking liquid to the wine mixture, then pour the mushroom soaking liquid through a fine-mesh strainer into the wine mixture.
Step 3
When the aromatics are deeply browned, remove the roasting pan from the oven; reduce the oven temperature to 325°F. Bring the wine mixture to a simmer over medium-high. Nestle the short ribs meaty side down in the aromatics in the roasting pan, then add the wine mixture. Cover tightly with extra-wide, heavy-duty foil; if the pan has fixed raised handles, be sure to get a good seal around the base of the handles. Transfer to the oven and cook for 3½ hours.
Step 4
Remove the roasting pan from the oven and carefully remove the foil, allowing the steam to vent away from you; reserve the foil. Using tongs, flip each rib meaty side up. Return the pan, uncovered, to the oven and cook until a skewer inserted into the ribs meets no resistance, 45 minutes to 1 hour. Using tongs, transfer the ribs to a platter and tent with the reserved foil. Let rest for 20 minutes.
Step 5
While the ribs rest, set a fine-mesh strainer over a large saucepan. Scrape the contents of the roasting pan into the sieve; press on the solids to extract as much liquid as possible, then discard the solids. Tilt the pan to pool the liquid to one side, then use a wide spoon to skim off and discard as much fat as possible; you should have about 3 cups defatted liquid. Bring to a simmer over medium-high, then reduce to medium and cook until reduced to about 2½ cups, about 5 minutes. Meanwhile, in a small bowl, mix the flour and butter until homogeneous.
Step 6
With the liquid simmering over medium-low, whisk in the butter-flour mixture a spoonful at a time. Return to a simmer and cook, whisking often, until the sauce no longer tastes starchy and is thick enough to coat the back of a spoon, about 5 minutes. Off heat, taste and season with salt and pepper.
Step 7
Uncover the short ribs and pour on about half of the sauce. Sprinkle with the parsley. Transfer the remaining sauce to a serving bowl and serve on the side.
Step 8
Make-Ahead Instructions:Follow the recipe to braise the short ribs. When the ribs are fully tender, after removing the roasting pan from the oven, flip each piece meaty side down, then let cool completely. Re-cover the pan with the foil and refrigerate for up to 48 hours. To finish, use a spoon to remove and discard the solidified fat on the surface of the braising liquid and bring to room temperature. Put the pan, covered with foil, in a 350°F oven until the ribs are heated through, 20 to 30 minutes. Continue with the recipe to strain the cooking liquid (you will not need to skim the fat off the liquid after straining) and make the sauce.