In a large pot, bring 4 quarts water to a boil. In a large bowl, combine 3 quarts water, 2 tablespoons kosher salt and 1 quart ice and stir until the salt dissolves. Add 2 tablespoons salt and the broccoli rabe to the boiling water and cook until the rabe is bright green and crisp-tender, about 40 seconds. Using tongs, immediately transfer to the ice water. Let stand for 30 seconds, then remove from the ice water, throughly pat dry and cut crosswise into 1-inch pieces. Set aside.

Heat the broiler with a rack about 6 inches from the element. Line a rimmed baking sheet with foil.

Place the beef stew in a medium bowl, cover and microwave on high until hot, 1 to 3 minutes, stirring once halfway through. Using 2 forks, shred the meat into bite-size pieces. Taste and season with salt and pepper. Set aside.

In a 12-inch skillet over medium-high, heat the oil until shimmering. Add the rabe and cook, stirring occasionally, until lightly browned, 2 to 3 minutes. Add the garlic and pepper flakes and cook, stirring, until the garlic is light golden, about 1 minute. Transfer to a medium bowl and season with salt and pepper. Drizzle with the vinegar and toss to combine. Set aside.

Place the roll halves cut sides up on the prepared baking sheet. Broil until beginning to brown, about 1 minute. Divide the cheese evenly among the top and bottom halves, then continue to broil until the cheese is just melted, about 30 seconds. Divide the beef among the 4 bottom rolls, then arrange the rabe on the beef. Cover with the tops, then cut each sandwich in half.