Slice croissants horizontally and place all 4 on a baking sheet.
Fill a medium-sized frying pan halfway with water. Over medium heat, bring water to a simmer. Add white vinegar to water. Do not let water boil. Working with 1 egg at a time, crack egg into a small bowl and slide into simmering water. Simmer eggs 3 to 5 minutes, or until whites are cooked and yolk is still soft. Transfer eggs with slotted spoon onto a plate.
TIP: Eggs can be pre-cooked and refrigerated to this point. Reheat by sliding egg into simmering water for 1 minute at time of service.
In a small saucepan, add hollandaise packet to the milk. Add the chives and tarragon. Heat thoroughly over low heat, stirring constantly. Remove from heat. Set aside.
Separate croissant halves and place together forming a circle, cut-side up. Top each half with a slice of prosciutto and a poached egg. Spoon hollandaise sauce over the top of the egg. Garnish with tarragon leaves.