Bring a large pot of water to a boil. Prepare an ice water bath. Blanch the broccolini in the boiling water for 1 1/2 to 2 minutes. Immediately plunge into the ice water, then drain on paper towels.
In a large skillet, melt the butter over medium-high heat. Add the garlic and cook for a minute, then throw in the broccolini. Toss to coat in the butter and garlic, then sprinkle with salt and pepper. Add the lemon zest and juice and continue cooking for a couple more minutes.