Whisk the eggs in a bowl with the half-and-half, salt, and pepper.
Heat 1 tablespoon of butter in a large saute or omelet pan.
Add the eggs and cook them over medium heat, stirring constantly, until the desired doneness. Off the heat, add 1 more tablespoon of butter and stir until it's melted. Check for seasonings.
Serve hot on a slice of toasted brioche with 1 teaspoon of caviar per person.