for the Béchamel, melt butter in a small pan over medium heat. Once the butter phones, whisk in flour. Cook one minute.
Whisk milk into saucepan in a thin, steady stream until completely combined, then whisk in Dijon and nutmeg. Season with salt and pepper. Cook mixture until slightly thickened, 2 to 3 minutes.
For the bread pudding, layer a third of the bread cubes in bottom of a 4 to 6 quart slow cooker. Ladle a third of the Béchamel over bread. Top with half of the ham and half of the Swiss cheese.
Repeat layering on top with remaining bread cubes and Béchamel. Cover slow cooker and cook on high setting, 2 to 3 hours or low setting for 4 to 5 hours. Top with Gruyere during last 10 minutes of cooking to melt. Serve with sunny side up eggs. Makes 8 to 10 servings.