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1
Soak the mushrooms
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2
In a small bowl, soak porcini in 1-1/2 c warm water until softened, about 10 mins. Drain, reserving 1 c of soaking liquid. Coarsely chop mushrooms and set aside in a bowl.
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3
Braise ribs
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4
Season the short ribs with 1 tsp. salt and 1/4 tsp. pepper. In a 7-8-qt Dutch oven, heat 1-1/2 T of oil over med high heat until shimmering. Add short ribs, in batches, and brown all over, 2 to 3 min per side. Transfer to plate. Pour off and discard all but a thin layer of fat.
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5
Reduce heat to med and add the remaining 1 T oil to pan. Add onion, carrot, celery, and a pinch of salt and cook until the vegetables are tender, 4-5 minutes. Add tomato paste and bay leaf and cook, stirring, until the tomato paste darkens, 1-2 min. Add red wine and simmer, stirring and scraping up any browned bits with a wooden spoon, until almost evaporated, 2-3 min. Add reserved mushroom liquid and tomatoes and bring to a simmer. Add short ribs and any accumulated juices and porcini; cover, reduce heat to maintain a gentle simmer, and cook, turning the ribs every 40 min, until meat is fall-off-the-bone tender, 2-1/2-3 hours.
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6
Put ribs on a plate to cool. Pour sauce into a heatproof bowl and discard bay leaf. When fat rises to surface, skim off and discard. Season to taste with salt and pepper. When meat is cool enough to handle, remove and discard the bones and any fat or cartilage from meat. Shred meat and set aside in a medium bowl.
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7
Make a bechamel sauce
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8
Melt the butter in a 3qt saucepan over med heat. Stir in flour with a wooden spoon and cook until golden, about 2 min. Gradually whisk in milk and cook at a gentle simmer, stirring often, until the mixture thickens, about 10 min. Season with 1 tsp. salt. Mix bechamel sauce into short rib sauce.
