Blanch the broccolini in a large pot of boiling salted water for 2 minutes. Drain immediately and immerse in a bowl of ice water.
Melt the butter in a large saute pan. Add the lemon zest and garlic and stir. Drain the broccolini and add it to the garlic mixture and heat for 2 minutes. Add the lemon juice, 1/2 teaspoon salt and the pepper, and toss well before serving.
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