Melt the butter in a large skillet set on medium heat.
Add the minced garlic and sauté for a couple of minutes.
Add the fresh broccolini, coating it in the butter and garlic, and sauté for about 2 minutes.
Then add a couple of tablespoons of water to the pan, cover and let simmer until the broccolini is tender, yet still bright green (this should take only a few minutes).