Blanch the broccolini in a large pot of boiling salted water for 2 minutes. Drain immediately and immerse in a bowl of ice water to stop the cooking process for 2 minutes. Retransfer to the colander to drain.
In a large skillet over medium heat, melt butter. Add lemon zest and pressed garlic; stir constantly for 1 minute. Pour in lemon juice, stir to blend and add broccolini; toss to coat. Crack some freshly ground black pepper and toss until heat through, about 1 ½ minutes. Serve immediately.