Peel peanuts if necessary, chop coarsely or grind in a hand mixer. Fry in a frying pan until lightly browned. Remove and fill into a dessert bowl.
Peel the garlic, galangal and carrots. Rinse and clean the bell peppers, broccoli, leeks and chilies.
Chop the garlic and galangal into small pieces. Cut the carrots lengthwise into two-millimeter-thin slices, and these diagonally into three-centimeter-long pieces. Cut the leek diagonally into half-centimeter-wide pieces. Pick broccoli into small roses. Chop the bell peppers into bite-sized pieces. Remove seeds from chili peppers, chop very finely.
Rinse chicken breast fillet under cold water, dry and cut into narrow strips.
Heat half of the oil in a wok. Add garlic and galangal, let it color a little bit. Stir-fry the meat in several small portions until hot, remove and keep warm with aluminum foil with the lid closed. Heat remaining oil together with Thai basil paste. Stir-fry broccoli, carrots, bell bell pepper and leek for seven minutes until al dente. Add the meat and any juices that have escaped. Season with lime juice.
Arrange on a platter. Sprinkle with a small amount of chopped peanuts, the rest separately in a dessert bowl to bring to the table.