Bring a large pot of water to a boil and add 2 tablespoons kosher salt.
Cut off the thick broccoli stalks, and cut the broccoli into 1-inch florets with about 1 inch of the tender stalks. Reserve the stalks for another use. Add the broccoli to the boiling water and blanch until crisp-tender, about 3 minutes; do not overcook. Drain in a colander and rinse under cold water to stop the cooking; drain well and pat dry.
Put the pecorino in a large bowl and whisk in the warm water. Whisking constantly, slowly drizzle in the oil to make a loose emulsion. Add the broccoli and toss to coat. Season with Maldon salt, if necessary, and with pepper. Let stand for 30 minutes before serving.