Place the steak in the freezer for 20-30 minutes to firm it up, which makes slicing easier. Slice the steak as thinly as possible against the grain.
In a medium bowl, toss the sliced steak with the soy sauce until evenly coated. Set aside.
Heat the vegetable oil in a large skillet or cast iron pan over medium-high heat. Add the sliced onion and cook, stirring occasionally, until soft and lightly browned, about 8-10 minutes. Remove the onions from the skillet and set aside.
Add the steak to the same hot skillet. Spread it in a single layer, working in batches if necessary to avoid crowding the pan. Cook for 2-3 minutes, flipping once, until browned and cooked through. For safety, steak should reach an internal temperature of 145°F (63°C).
Return the cooked onions to the skillet with the steak. Stir everything together to combine.
Divide the steak and onion mixture into four equal portions within the skillet. Lay two slices of provolone cheese over each portion. Let the cheese melt, which should take about 1 minute.
Slice the hoagie rolls lengthwise, but not all the way through. Gently open a roll and place it face down over one of the cheesy steak portions in the pan.
Use a spatula to slide under the steak and cheese, and scoop the entire portion into the roll. Repeat for the remaining sandwiches.
Serve immediately while warm.