In a small pot over medium to high heat, melt the butter. Continue cooking until it starts to bubble and turn slightly brown, approximately 1 minute. Slowly add flour, continually whisking until it starts to clump. Slowly add milk and continue whisking until sauce is smooth and velvety in texture, approximately 1 minute more. Add nutmeg, salt and pepper. Stir well and remove from heat and leave covered until needed.
- Heat oven to 375°F (190°C). Slice bread, butter all sides and place 2 slices on a large baking sheet, lined with parchment paper. On top of each, place a slice of ham followed by a handful of cheese, fully covering the ham. Close sandwich with remaining bread, top with another slice of ham and remaining cheese.
- Toast the sandwiches in the oven for 4 to 5 minutes, or until the cheese is melting and starting to brown. Remove from oven and evenly spoon béchamel sauce over sandwich to completely cover them.
- Set oven to broil on high temperature. Once heated, return sandwiches to oven and broil for 2 to 3 minutes, or until sauce and cheese are bubbling and starting to brown. Take care to watch the sandwiches closely to ensure they don’t get burned. Remove from oven.
- Heat oil in a medium frying pan over medium to high heat. Cook eggs to preference. For Sunny Side Up, crack both eggs and fry for approximately 2 to 3 minutes or until the whites are set while the yolks remain soft. Place one egg onto each sandwich, garnish with chives and serve hot.
Pair with a Sancerre or Riesling to bring out the flavours of the ham and cheese.