Heat oven to 400°F.
Combine the pickles, pickle brine, ginger, garlic, chili sauce, and sesame oil. Allow pickles to marinate while you deal with the broccoli.
Toss the broccoli with the olive oil and salt, spread into an even layer on a half-sheet pan, roast for 15 minutes. Toss and roast for another 15 minutes. When you remove the broccoli from the oven, move a rack under your broiler and heat the broiler to high.
Split and lightly toast the hoagie rolls under the broiler for 1 to 2 minutes.
For each sandwich: Spread mayonnaise on one side and top with 1/4 cup of the pickle mixture, then scatter on 1/4 cup of fried onions. Put the roasted broccoli on the other side and sprinkle with 1 ounce of the cheese. Broil, open-faced, for 2 minutes. Close the sandwich and enjoy.