Heat the oven to 350 degrees F.
Grease a 9 x 13-inch baking dish with butter.
Beat the eggs in a large bowl.
Whisk in the milk and cream, season with salt and pepper.
Fold in ham, pecorino and fontina cheese, leaving ½ cup of the fontina cheese for topping, add herbs and mix.
Arrange half of the bread cubes evenly over the bottom of the buttered baking dish.
Pour over half of the egg mixture.
Add a second layer of bread cubes then pour the remaining egg mixture over the top and sprinkle with the remaining ½ cup of fontina.
Bake strata in oven for about 45 minutes.
Let rest for 10 minutes before serving.