How to Make It
On a griddle, melt the butter. Cook the ham over moderate heat, turning, until golden and crispy around the edges, about 5 minutes.
In a shallow bowl, whisk the eggs with the milk. Dip the bread in the eggs and cook on the griddle until golden on the bottom, about 3 minutes. Flip the bread and top with the cheese and ham. Cover and cook until the cheese is melted. Garnish with basil and serve.