In a large skillet, heat 1 1/2 tablespoons olive oil over medium heat. Add the onions and season with salt and pepper. Cook until golden, about 10 minutes. Transfer to a bowl; reserve the skillet.
Meanwhile, in a medium bowl, whisk together 2 1/2 tablespoons olive oil, the lemon juice and 1/4 teaspoon each salt and pepper. Using a food processor fitted with a shredding disk, shred the carrots and broccoli stalks. Toss with the dressing.
Spread the cream cheese on the roll bottoms and top with the onions. In the reserved skillet, heat the remaining 2 tablespoons olive oil over medium-high heat. Add the steak, season with salt and pepper and cook, stirring, until barely pink, 2 to 3 minutes. Divide the meat among the roll bottoms, pour any pan juices on top and set the roll tops into place. Serve with the carrot-broccoli slaw.