Preheat oven on high broil.
Cut the French baguette into one-inch slices.
Hollow out the middle of the bread slices and save the removed portion of bread for homemade breadcrumbs or croutons.
Brush each bread slice with the herb, melted butter, and extra virgin olive oil mixture.
Crack an egg over each slice of each prepared slice of bread.
Add lots of shredded cheese and a tomato slice or slices of tomatoes.
Arrange the loaded slices of bread on a baking sheet and place it on the middle rack of a preheated oven set on high broil.
Broil until the bread is golden brown, the cheese is melted, you can't take it anymore.
Remove from the oven and serve immediately.