Preheat the oven to 400 degrees.
Combine the pickles and brine, garlic, ginger, chili sauce and toasted sesame oil in a medium bowl. Marinate at room temperature while you make the sandwiches.
Toss together the broccoli, oil and salt on a large baking sheet; roast until the broccoli is bright green, is starting to brown on the edges and is easily pierced with a fork but not soft, 15 to 20 minutes. Let cool.
Position an oven rack 4 to 6 inches from the broiler element; preheat the broiler.
Split the rolls, leaving them hinged. Open them and set on a large baking sheet and lightly toast under the broiler, 1 to 2 minutes; watch closely to keep them from burning.
To assemble the sandwiches, lightly spread mayonnaise on the insides of the rolls. Divide the roasted broccoli evenly among them. Use a slotted spoon to lift the pickles out of their marinade and evenly distribute them on the broccoli, then layer the fried onions and ricotta salata on top.
Serve the pickle marinade with the sandwiches, for dipping.
Make Ahead: The pickles can marinate in the refrigerator for up to 5 days in advance.
Sprinkle on some toasted pine nuts, too, if you feel like it.