Cut the kale into bite-size pieces, removing any tough stems. Rinse and shake dry.
Warm the oil and garlic in a large stockpot over medium-high heat. Remove the garlic as soon as it browns (don't let it burn). Add the kale and stir-fry 5 minutes. Add 1/4 cup water, cover, and cook 8 to 10 minutes or until tender. Uncover and add the sugar, salt, olives, and peppers. Cook over medium-high heat until the liquid has evaporated.
Spoon into a serving dish; scatter the garlic over the top. Drizzle with the balsamic vinegar. Serve warm or at room temperature.