Combine the first 4 ingredients in a medium bowl; cover and marinate in refrigerator 30 minutes.
Remove the roots, outer leaves, and tops from leek, leaving 1 1/2 to 2 inches of dark leaves. Rinse leeks with cold water, and cut into 2-inch julienne strips to yield 1 1/4 cups.
Heat oil in a large nonstick skillet over medium-high heat. Add ginger and garlic; sauté 1 1/2 minutes. Add beef mixture; sauté 5 minutes. Add leek, onion, pepper, and salt; sauté 3 minutes. Serve over rice.