Carrot-Beef Sushi with Caper-Basil Mustard

Preheat oven to 350°F with rack in middle.
Heat a dry 12-inch heavy skillet (not nonstick) over medium-high heat until hot, about 2 minutes. Meanwhile, pat steaks dry and sprinkle all over with 1/2 teaspoon each of salt and pepper (total).
Add vegetable oil to hot skillet, swirling to coat bottom, then brown steaks, turning once, about 4 minutes total. Transfer steaks to a small shallow baking pan and roast in oven 5 minutes. Transfer to a cutting board and cool about 30 minutes.
While steaks cool, cut carrots lengthwise into 42 (1-inch-wide) ribbons (less than 1/16 inch thick) with an adjustable-blade slicer or a vegetable peeler.
Cook ribbons in a pot of boiling salted water (2 tablespoons salt for 4 quarts water), uncovered, until just tender, about 3 minutes. Transfer with a slotted spoon to an ice bath to stop cooking. Carefully drain, then pat ribbons dry.
Whisk together basil, parsley, mustard, shallots, capers, and garlic in a small bowl, then add oil in a slow stream, whisking until emulsified.
Trim fat and gristle from steaks, then cut each lengthwise into 3 (3/4- to 1-inch-wide) strips.
Place a sushi mat with slats running crosswise or a 9-inch square of parchment paper on a work surface. Arrange 6 to 8 carrot ribbons side by side lengthwise, following slats and slightly overlapping, to form a 6-inch square.
Spread about 1 tablespoon of mustard sauce evenly across bottom half of carrot square, then lay 1 strip of steak across carrots 1 inch from edge nearest you. Roll up carrots and beef tightly, using sushi mat as an aid.
Transfer beef roll, seam side down, to a cutting board, then trim ends and cut crosswise into about 10 (1/2-inch) pieces. Make and cut 5 more rolls. Turn pieces upright to serve.