Mix chopped parsley, garlic, and lemon zest in small bowl. Set aside.
Add 1 inch of water to medium pot and bring to rapid boil over medium-high heat. Add eggs in a single layer in the pan.
Cover the pan with a lid and set a timer for 6 minutes, 30 seconds. The water in the pan should almost immediately return to a simmer.
When the timer goes off, remove the lid and eggs and immediately place the eggs in a bowl of water with ice. Allow eggs to sit for 1-2 minutes. This will completely stop the cooking.
Starting at the large end of the egg, carefully crack and peel the shell. Place peeled eggs on a plate. Carefully cut each egg in half and top with a generous dollop of caviar, a sprinkling of gremolata, and salt and cracked pepper to taste.
Serve with a side of creamy avocado toast and a glass of Champagne or sparkling wine for a decadent breakfast.