Break the eggs into a large mixing bowl, reserving 2 yolks in a separate bowl. To the large mixing bowl add the fines herbes, salt, and pepper. Combine with a whisk.
Combine the heavy cream and the mustard with the reserved egg yolks and mix well.
In a heavy saute pan over medium-low heat, melt the butter. When the butter is melted, add the whole egg mixture and cook, stirring constantly, until creamy and slightly thickened.
Add the yolk mixture and the tomatoes to the slightly thickened egg mixture And remove from the heat while continuing to stir constantly. The heat in the pan will continue to cook the eggs. Perfectly scrambled eggs should be creamy with very soft curds. Sprinkle with the chives and serve.