While it is sometimes called "baby broccoli" and in fact looks like it might be a vegetable that was simply picked very early, broccolini is actually a fully mature example of a variety called Italian sprouting broccoli.
It's got the same delicious mixture of sweet and bitter that regular broccoli has, but in a form that is concentrated more on the long leggy stems than fully flowering heads. The main drawback with most broccolini is that those stems can get big and tough enough that they need to be peeled. After that, no problem.
How to choose: Look for broccolini that has fresh bases (not dried out), firm stems (no soft spots) and tightly furled heads (no evident flowering).
How to store: Refrigerate broccolini in a tightly sealed plastic bag.
How to prepare: Blanch it, chop it and sauté it with olive oil, dried red pepper flakes and garlic to make a quick winter pasta sauce.