Make the pickles: Combine ingredients; let sit for a couple hours.
Prep the broccoli: Preheat oven to 375° F. Combine broccoli, olive oil, and salt; mix thoroughly, adding more oil if necessary to give each piece a light sheen. Taste a piece of the raw broccoli and adjust seasoning if necessary.
Roast: Spread broccoli onto a baking sheet in one layer and roast for about 10-12 minutes, or until the broccoli is tender but with still a little bit of crunch in the center, and starting to get dark on the edges. Remove from the oven and let cool, or make subs right away.
In a 375° F oven, toast the hero rolls and reheat the broccoli, if needed.
Spread 2 tablespoons of mayo on each of the sub rolls; stuff the rolls with the roasted broccoli.
Top and go: Top each sandwich with a little bit of the lychee muchim. Sprinkle on the ricotta salata, pine nuts, and fried shallots.