Place sliced leeks in a large bowl of cold water. Let stand for 5 to 10 minutes to rid them of dirt and sand. Lift out of water with a slotted spoon and drain.
In a large nonstick skillet, heat olive oil over medium-high heat. Add leeks and other remaining ingredients and cook, turning the vegetables frequently, until browned, about 15 minutes.
Reduce heat to medium and continue to cook until vegetables are tender, about 10 minutes. Adjust seasonings; serve immediately.