Prepare the Brioche: Lightly toast the slices of brioche until golden brown. While still warm, rub the toasted bread with freshly grated lemon zest and brush lightly with olive oil. Set aside.
Poach the Eggs: Bring a pot of water to a gentle simmer and add the vinegar. Crack each egg into a small bowl and slide them one by one into the simmering water. Poach the eggs for 3-4 minutes, until the whites are set and the yolk is still soft. Remove with a slotted spoon and drain on a paper towel.
Assemble the Dish: Place a poached egg on each slice of lemon zest brioche. Top each egg with a small spoonful of caviar, allowing the pearls to sit delicately on the surface of the egg.
Garnish: Sprinkle the dish with finely chopped chives or microgreens, and finish with an extra sprinkle of lemon zest and a light drizzle of olive oil.
Serve and Enjoy: Serve immediately, with a side of fresh fruit or a light salad for a complete, elegant breakfast.