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 1 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 the garlic and pepper flakes from burning.