One 4-pound chuck eye roast or other chuck roast, tied
Kosher salt and freshly ground pepper
All-purpose flour, for dusting
1/4 cup extra-virgin olive oil
1 large onion, coarsely chopped
3 garlic cloves
6 slices ginger
3 cups beef stock or low-sodium broth
1/2 cup mirin
1/2 cup soy sauce
1/2 star anise pod
1/2 pound shiitake mushroom caps
1 pound large carrots, sliced diagonally 1/2 inch thick
1 1/2 pounds daikon, peeled and cut into 2-inch chunks
1 1/2 teaspoons cornstarch mixed with 2 tablespoons water
Preheat the oven to 300°. Season the roast with salt and pepper and dust with flour. In a medium, enameled cast-iron pot, heat 2 tablespoons of the oil. Add the roast; cook over moderate heat, turning, until browned all over, 20 minutes. Transfer to a plate.
Add the onion, garlic and ginger to the pot and cook, stirring, until softened, 5 minutes. Add the stock, mirin, soy sauce and star anise and bring to a boil. Return the meat to the pot, cover and transfer to the oven. Braise for 2 1/2 hours or until tender, turning once halfway through.
Meanwhile, in a medium skillet, heat the remaining 2 tablespoons of olive oil. Add the mushrooms, season with salt and pepper and cook over high heat until golden, about 8 minutes.
Transfer the roast to a plate. Strain the cooking liquid into a bowl; discard the solids. Skim off the fat and return the liquid and meat to the pot. Add the mushrooms, carrots and daikon. Cover and braise in the oven for 45 minutes, until the vegetables are tender.
Transfer the roast to a work surface. Using a slotted spoon, transfer the vegetables to a deep serving platter; cover. Boil the liquid until reduced to 3 1/2 cups. Stir the cornstarch slurry and whisk it into the simmering liquid until thickened.
Remove the strings from the roast and cut into thick slices; arrange on the platter and pour the sauce on top.