To make slicing it easier, freeze the beef for 30 minutes to firm up.
Preheat a double-burner griddle or two large skillets over medium-high heat. Thinly slice the meat against the grain.
Toss the onions in a bowl with the oil and put them on the griddle. Cook for a few minutes, stirring occasionally, until the onions become translucent. Push the onions to the back of the griddle.
Place the beef on the griddle and season with salt and pepper. Cook, turning occasionally, until no pink remains. Stir the onions into the beef and chop the beef mixture into bite-size pieces with the side of a metal spatula.
Divide the beef and onions between the hoagie rolls. Top with the provolone and cheese sauce. Serve immediately, topped with giardiniera, if desired.