Broccolini is a hybrid of broccoli and gai lan (Chinese kale or broccoli). It has smaller florets and thinner stalks than broccoli and the flavour is a little milder. It lends itself to just about any cuisine. Here are 2 simple recipes.
Broccolini with lemon:

Wash and trim the broccolini and set aside. Warm a generous amount of olive oil in a heavy frypan over low heat and then add some strips of lemon rind and some sliced garlic. Allow them to become fragrant but not to brown before adding the broccolini. Season with salt and freshly ground black pepper. Allow the broccolini to cook, turning occasionally, until the stems are just tender. Add a splash of lemon juice and serve.
Roasted miso broccolini:

Preheat your oven to 220ºC (425°F). In a large bowl, whisk 1 tablespoon of white miso paste, 2 tablespoons of oil (I used peanut), 1 tablespoon of mirin (sweet cooking sake), 1 tablespoon of grated ginger, 1 minced clove of garlic, some freshly ground black pepper to taste and ¼ of a teaspoon of red pepper flakes until well-combined. Add 2 bunches of washed and trimmed broccolini to the bowl and toss them until coated with the miso mixture. Transfer to a baking tray and arrange in a single layer. Bake for 10 minutes, turning once. Remove from the oven and serve immediately.