Dice potato into 1/2-inch cubes and boil in salted water until fork tender. Drain and set aside.
Cut the white part of the leeks in half lengthwise, wash and cut into pieces.
Heat pan with olive oil, add chopped garlic and leeks and sauté for 2 minutes, add vegetable broth, boil for 10 minutes, add potatoes, add more broth if needed. Season with salt and pepper.
Thicken with a cornstarch solution, let it come to a boil, add heavy cream, boil one time only.
Season to taste.