1. Place eggs in large saucepan and cover with cold water by 1 inch. Bring to a boil, remove from heat and cover for 7 minutes. Drain hot water from pan and fill with cold water, cool.
2. Mix rice and red wine vinegar in medium bowl. Season with salt and pepper. Divide into 6 bowls.
3. Cut ham into 1 1/2-2 inch pieces. Heat skillet over medium heat and sear on each side until lightly browned, about 2 minutes per side.
4. Peel eggs and cut in half. Arrange eggs, ham and avocado on rice and serve immediately.