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For the Braised Flank Steak, preheat oven to 350°F. Season steak on both sides with salt and pepper. Heat oil in large heavy-bottom ovenproof skillet on high heat. (Pan should be just large enough for the flank steak to fit flat on the bottom.) Add flank steak. Cook 5 to 7 minutes per side, until well browned. Remove and set aside.
Reduce heat to medium-high. Add carrot, onion and garlic; cook and stir just until vegetables are lightly browned but still firm, about 3 minutes. Return steak to pan. Mix beef stock, 2 tablespoons of the Mustard, tomato paste and thyme in large bowl until well blended. Pour over steak and vegetables. Cover and transfer pan to oven.
Braise about 2 1/2 hours, until steak is tender and shreds easily with a fork.
Meanwhile, for the Mushrooms, heat 2 tablespoons of the olive oil in large skillet on medium-high heat until shimmering. Add about half of the mushrooms to skillet. Cook 2 minutes without stirring. Turn mushrooms over. Add half each of the butter and garlic; cook about 2 minutes longer or until mushrooms are tender. Transfer to paper towel-lined plate. Repeat with remaining mushrooms, butter and garlic. Set cooked mushrooms aside.
For the Cauliflower, cut each quarter into very thin slices. Place remaining ingredients in large bowl; mix well. Add cauliflower. Cover. Marinate at least 1 hour or until ready to serve.
Remove steak from pan; transfer to clean cutting board and let rest. Using a slotted spoon, remove and discard onion and carrot. Return pan to stovetop. Bring braising liquid to simmer on medium-low heat. Simmer until reduced by about half. Whisk in remaining 1 tablespoon Mustard until well blended. Coarsely shred steak using 2 forks, then chop into 3-inch pieces. Return steak to pan, stirring to coat with sauce.
To assemble sandwiches, spread additional Mustard on cut sides of rolls. Layer bottom half of each roll with Steak, Mushrooms, Cauliflower and arugula. Top each with remaining half of roll. Cut in half to serve.
Test Kitchen Tips:
•To prepare steak in Instant Pot®, heat oil in pot on SAUTÉ setting. Sear steak 5 to 7 minutes per side. Remove steak from pot; set aside. Add carrot, onion and garlic to pot, cooking about 3 minutes, or just until browned but still firm. Return steak to pot. Mix beef stock, 2 tablespoons of the Mustard, tomato paste and thyme in large bowl until well blended. Pour over steak and vegetables. Close lid. Set valve to seal. Set to cook for 60 minutes on MEAT/STEW function or until meat is tender. When done, quick-release the pressure. Open the lid once pressure inside the pot is completely released. (Check manufacturer’s manual for safe operating directions.) Remove steak from pot; transfer to clean cutting board and let rest. Using a slotted spoon, remove and discard onion and carrot. Set Instant Pot to SAUTÉ setting and simmer cooking liquid until reduced by about half. Whisk in remaining 1 tablespoon Mustard. Shred and cut meat as directed above and return to pot with sauce.
•To save some hands-on cook time, try roasting mushrooms in the oven. Place mushrooms in large bowl. Drizzle with only 2 tablespoons olive oil and toss with garlic. Spread mushrooms evenly on large parchment-lined sheet pan. Roast in preheated 450°F oven about 15 minutes or until browned and tender, turning halfway through cooking. Melt butter and drizzle over roasted mushrooms. Set aside until ready to serve.
•For an easy shortcut, store bought giardiniera works great in place of the marinated cauliflower.