Hard-boil the eggs: Place the eggs in a pot with water to cover, bring to a boil, then lower the heat to a simmer and simmer for 10 minutes. Run the cooked eggs under cold water and peel. Cut each egg in half the long way and remove the yolk.
In a blender or food processor fitted with the metal blade, combine the yolks, oil, parsley leaves, a generous amount of pepper, and the anchovy paste. Process until fluffy. If the mixture looks dry, add a little more oil. Stuff each egg white with a generous spoonful of the yolk mixture and refrigerate until just before serving. Garnish with additional parsley and cherry tomatoes.