PLACE potatoes in medium saucepan. Cover with water. Add salt; bring to a boil. Cook until soft (about 30 minutes); drain thoroughly and mash with potato masher. Add white pepper; mix well.
HEAT1 tablespoon annatto oil in small skillet over low heat. Add onion; cook, stirring occasionally, for about 4 to 5 minutes or until very soft. Add onions to mashed potatoes; mix well. Let mixture cool for about 10 minutes. Stir in cheese. Season with salt, if desired.
SCOOP potato mixture with 1/3 cup measure and shape into 8 patties about 3 inches in diameter and 1/2 inch thick. Place on large plate or baking sheet. Cover with plastic wrap; refrigerate for about 15 minutes.
HEAT nonstick griddle or large skillet over medium heat. Brush one side of patties with remaining annatto oil. Place on griddle and cook until browned and crispy on the bottom, about 8 to 10 minutes. Brush tops with additional annatto oil; turn over with spatula to brown on other side. Patties should have crispy brown crusts with tender insides.
PLACE shredded lettuce and carrots, olive oil and lemon juice in medium bowl; mix to coat.
TO SERVE: Line platter with salad; top with patties. Top patties with Peanut Sauce and chopped egg. Serve with additional Peanut Sauce, if desired.
*NOTE: You can make annatto oil by heating 2 tablespoons annatto (achiote) seeds in 1/2 cup olive or vegetable oil over low heat for 3 to 5 minutes, stirring occasionally until oil turns bright orange. Store in small jar or container. Or, you can substitute 2 tablespoons olive or vegetable oil combined with 1 teaspoon ground annatto or sweet paprika for the 2 tablespoons annatto oil.