For the marinade: Combine the soy sauce, sugar, sesame oil, mirin, pepper, garlic and scallions in a large bowl. Whisk until the sugar dissolves. Add 4 cups of water and whisk to combine. Add the shaved beef and toss to combine. Cover with plastic wrap and refrigerate for at least 8 and up to 24 hours, tossing several times.
For the pickled cucumbers: Whisk the vinegar, oil, sugar, salt and Sriracha in a medium mixing bowl until the sugar has dissolved. Remove the cucumber ends. Then cut the cucumbers into slices about 1/4-inch thick. Add the cucumber slices to the bowl and toss to combine. Cover with plastic wrap and refrigerate for at least 8 hours and up to 24 hours before serving.
After marinating, remove the meat and pickles from the refrigerator and allow them to sit out at room temperature while you make the cabbage slaw.
For the cabbage slaw: Whisk together the vinegar, sesame oil and sugar in a large bowl until the sugar has dissolved. Whisk in the canola oil until emulsified. Add the cabbage and toss to combine. Season with salt and pepper. Set aside.
Drain the marinade from the meat using a large mesh strainer, discarding the marinade. Heat a large cast iron or saute pan over medium-high heat. Add 2 tablespoons of the canola oil to the pan, swirling the pan to coat. Scatter half of the beef in an even layer in the pan, and sprinkle with 1/4 teaspoon of kosher salt. Continue until it is just cooked through and caramelized in parts, flipping once, 2 to 3 minutes. Transfer the cooked meat to a plate. Remove any liquid from the pan to a small bowl and wipe out the pan. Add the remaining canola oil to the pan and cook the rest of beef, seasoning with another 1/4 teaspoon of salt.
For the sandwich: Evenly divide the cabbage slaw among the 4 toasted hoagie rolls. Top each roll with meat and the sliced pickled cucumbers. Serve immediately.