In bowl, whisk together green onions, lime juice, brown sugar, Worcestershire sauce, ginger, vegetable oil, salt, thyme, allspice and cayenne. Toss with beef and marinate for at least 1 hour and up to one day.
Assemble one piece of beef and one pineapple chunk onto each skewer. Arrange in a single layer on a greased, foil-lined baking sheet. Broil on high, turning once until beef is browned and pineapple starts to caramelize, about 4 to 8 minutes.
Chef’s tip: For larger skewers, add 1-inch (2.5 cm) pieces of green onion and cubed red pepper to each skewer.