Prepare the cabbage rolls: In a small saucepan over medium-low heat, add the onions, olive oil, and ¼ teaspoon kosher salt. Cook, stirring frequently, until the onions turn a deep brown, 40–45 minutes. Remove from heat and let cool.
Meanwhile, bring a large pot of salted water to boil over high heat, and prepare a large ice bath. Using a paring knife, make four 1-inch-wide angled cuts around the stem end of the cabbage, surrounding the core; pull the core out and discard. Add the cabbage to the boiling water, core side down. Let it cook until the top leaves start to separate from the head, 1–2 minutes. Using tongs and keeping the cabbage submerged in the water, carefully separate the leaves from the head. Continue to cook each leaf until just tender at the rib, 3–5 minutes; remove and transfer the leaves directly to the prepared ice bath. Lift the leaves from the ice bath and transfer to a large plate; set aside while you prepare the filling. (Maintain the water at a low boil and reserve the ice bath.)
Preheat the oven to 400°F, and grease a 2-quart (7x9-inch) baking dish with olive oil.
Briefly soak the bread crumbs in the milk to moisten. In a large bowl, add the lamb, pan-cetta, Parmigiano, bread crumbs and milk mixture, caramelized onions, parsley, mint, egg, cayenne, and the remaining ½ teaspoon salt. Mix well with hands until combined.
On a wide work surface, lay out 8 large cabbage leaves, reserving any leftovers for another use. Spoon ¼ cup of the meat mixture into the center of each leaf, then roll the leaves tightly to form logs. Fold and tuck the ends to seal, if desired. Transfer to the prepared baking dish, and bake until the leaves are just browned at the edges and the filling is cooked through (it should register 155°F on a meat thermometer), about 25 minutes.
Meanwhile, make the tahini sauce: Plunge the parsley into the boiling water, and cook until it is fully wilted and bright green, 2–3 minutes. Use a slotted spoon or spider skimmer to transfer the parsley to the ice bath, then drain and discard the water. In a blender, add the blanched parsley, ¼ cup of cold water, olive oil, and ¼ teaspoon kosher salt. Blend on high until smooth.
In a medium bowl, add the tahini, lemon juice, and 1 tablespoon of cold water. Whisk slowly to combine (at this point, the mixture will seize up and tighten); drizzle in an additional tablespoon of water, bit by bit, while continuing to whisk, to thin mixture out until you have a creamy and thick sauce. Add the parsley purée and stir until smooth. Season with more kosher salt, if desired. Drizzle the cabbage rolls with the sauce (or put the sauce beneath them), and serve hot.