clean and sauté the leek
Clean the leeks and cut off the green parts (use those for a homemade leek soup). Cut into 10-12 cm or 4-inch chunks. Place a skillet with olive oil over medium heat. Add the leek and sauté for 2 - 3 minutes, turning the leek as it cooks.
braise the leeks
Add the butter and vegetable broth to the leeks. Season with salt and thyme. Bring to a boil over medium heat, then lower the heat to the minimum, cover with a lid and cook for 20 - 25 minutes or until the leeks soften.
cook the egg
Pour 1 liter (4 cups) water into a saucepan, place over high heat and bring to a boil. Using a spoon, dip an egg three times into the boiling water for about 2 seconds to prevent the egg from cracking. Reduce the heat and cook the egg at medium for 10 - 12 minutes. Drain the egg and cool it under cold running water.
Transfer the leek to a serving plate. Don't add all the liquid, only a couple of tablespoons. Sprinkle with cottage cheese and grate the hard-boiled egg over the leeks. Drizzle with olive oil, and serve.