Wash the broccolini and gently shake dry. Don't overdry as the little droplets of water left over help steam the broccolini. Trim the bottom 2 inches or so (the really stalky bits) and discard.
Peel the garlic cloves and break them open with the flat of a chef's knife.
Heat the oil (or whatever fat you're using to cook with. I like oil for this one) over a low heat in in a pan large enough to accommodate the broccolini without crowding. Add the garlic and let it gently saute, stirring occasionally so the garlic browns, but does not burn. If the garlic burns, start over. The point is to let the broken garlic flavor the oil, so keep the temperature low. Cook for around 5-10 minutes.
At this point you can throw out the garlic or leave it in.Add the broccolini and, using a pair of tongs, toss it in the oil, adding more if needed. Then season with salt & pepper and chili flakes and toss again. Increase the heat to medium.
Cook for 5-10 minutes, tossing occasionally (don't let that garlic burn!). Cook until the steams are tender, but not wilted. Serve immediately.