In a saucepan, cover the eggs with cool water by 1-inch and ½ tsp of salt. Bring the water to a full rolling boil over high heat then reduce the heat to medium-high. Cover the pan and continue cooking for 8 minutes. Transfer the eggs to a large bowl with ice-cold water. Let them cool down a bit then peel. Set aside.
In a large skillet, heat ½ cup of oil over medium-high heat to 360°F. Fry the eggs until the skin turns golden brown for about 1 minute. Remove the eggs from the pan and set aside.
In a food processor or blender, add tomato, shallots, garlic, and red chili peppers. Pulse until smooth.
In a large skillet, heat 3 tbsp of oil over medium-high heat. Cook the puree Sambal Balado, bay leaves, and kaffir lime leaves until fragrant for about 3 minutes or until oil separates.
Add salt, sugar, and return the eggs into the skillet. Lower the heat to medium, add a small amount of water if needed, simmer, and stirring occasionally for about 4 minutes or until the sauce is thickened to your liking. Taste and adjust the seasoning with additional salt and sugar if necessary.