In a large pot, cook the butter with the flour on medium heat, stirring with a wooden spoon for 2 minutes. Add the milk and nutmeg and, using a whisk, stir constantly until the milk is hot (but do not let it boil). Add salt and pepper. Let cool.
Place the 4 pieces of bread on a baking sheet covered in parchment paper. Add the parsley to the bechamel sauce and stir.
Spread the bechamel sauce on the bread. Top with ham and sprinkle with the grated cheese. Cook in the centre of the oven for 6-8 minutes or until golden brown. Serve garnished with avocado slices.