Cut or tear collard leaves off stems. Clean by rinsing repeatedly in cold water. Drain. Cut into two-inch strips. Place in a large pot, cover generously with vegetable broth (reserve 1/3 cup broth for later), and bring to a low boil. Cook until collards are almost tender, about 20 minutes. Drain and set aside.
Heat olive oil in a large frying pan over medium heat. Sauté garlic for two minutes, or until tender. Using slotted spoon, remove garlic to a bowl. Add diced leeks to pan, and sauté until tender, about 10 minutes—do not brown. Remove leeks to garlic bowl. Add pancetta to frying pan, and sauté until browned.
Return garlic and leeks to pan. Add reserved vegetable broth and collards. Stir gently and thoroughly until collards are completely cooked, about three minutes. Serve.