Trim the broccolini, taking about 1 inch off the bottom of the stalks. Slice any thick stalks lengthwise so they cook evenly.
Heat the butter in a skillet over medium heat. Add the garlic and cook for 1-2 minutes, until it softens and starts to brown.
Add the broccolini and mix to coat with the butter. Cook for about 2 minutes.
Add the chicken broth, salt and pepper and bring to a simmer. Reduce the heat to low and cover. Cook for about 15-20 minutes, or until broccolini is tender.
Check on the broccolini every 5 minutes or so to ensure the liquid has not evaporated. If it has, add an additional ⅛ cup of broth and continue cooking (covered).
Squeeze the juice of half a lemon on top and serve.
If the broth cooks off before broccolini is tender, add an additional ⅛ cup and continue cooking until tender.
Slice the stalks in half lengthwise if they are thick so they cook more evenly and become tender;
Add additional salt to taste, but note the lemon juice adds a salty flavor so be careful with the salt.
Store in the fridge for up to 3 days in a covered container.
How to freeze: Blanch the broccoli in boiling water for about 1 minute. Drain thoroughly and place on a baking sheet directly in the freezer for 3 hours. Place in a freezer bag and store up to 6 months. Cook from frozen or thaw overnight in the fridge.