Trim the ends of the broccolini stalks. If the stems are thick, slice the stalks in half lengthwise. In a high-sided pan with a lid, heat the oil over medium heat. When very hot, add the garlic and cook until soft. Add the broccolini and cook, stirring, until coated in oil, about 2 minutes. Add 1/4 cup water to the pan, turn the heat down to low, cover with the lid, and let simmer for 10 minutes.