Cut the top off the foccacia and hollow out the bread inside. Tear the top of the foccacia and the inside bread into 1-inch pieces and save for the egg mixture. Brush the inside of the foccacia with the Meyer lemon olive oil. Place on a baking sheet and toast for 10 minutes.
Meanwhile, in a large bowl, whisk the eggs. Add the basil, cheese, salt, pepper, and milk. Whisk lightly. Stir in up to 4 cups of the bread pieces.
Carefully pour the egg mixture into the toasted foccacia bottom. Return to the oven and bake until the eggs have cooked, about 35 to 40 minutes.
Cut the baked foccacia into 6 to 8 pieces and serve immediately.