Separate the kale into leaves, trim and rinse well. Drain thoroughly in a salad spinner.

Heat half the olive oil in a large, wide pot over medium heat and cook the garlic until soft. Stir in the orange wedges and cook together for a minute.

Add the kale, in batches if necessary, stirring it up so that the garlic and orange wedges are distributed evenly among the kale leaves. As the kale wilts, add more, mixing again, until all of it is inside the pot. Cover and cook for about 15 minutes, until the kale is tender. Season to taste with salt and pepper.

Remove from heat and drizzle in remaining olive oil. Serve hot, warm or at room temperature.