Trim the broccolini and cut it into 1-inch pieces, using the stems and the florets.
Heat the olive oil over medium-high heat in a large skillet (with a lid), the biggest one you have; you could also use a wok. Add the broccolini and cook, stirring to flip the pieces around occasionally, until they start to turn golden brown, but are still crisp tender, about 8 minutes. Season with salt, and add the garlic and the red pepper flakes, and sauté for one more minute, until you can smell the garlic.
Add the wine and cover the pan for 2 minutes, allowing the liquid to come to a simmer. Remove the lid and sauté for another minute until the liquid is almost evaporated and the broccolini is as tender as you like it. Remember that it will soften a bit more off the heat. Serve hot.
Notes
You’ll see that the garlic and pepper flakes are added towards the end – this lets you cook the broccolini over nice high heat, but prevents that garlic and pepper flakes from burning.