Trim 1 bunch broccoli; peel the stems and quarter the bunch lengthwise. Toss with olive oil; season with salt and pepper. Grill until charred and tender, 2 to 3 minutes per side. Whisk 3 tablespoons olive oil, the zest and juice of 1 lemon, 1 tablespoon each grated pecorino and water and 1 teaspoon dijon mustard; season with salt and pepper and drizzle over the broccoli. Top with shaved pecorino.