1. Melt butter in a 1 qt saucepan over medium-high heat. Add flour and whisk for about 1 minute until smooth.
2. Slowly pour in milk (cold) while whisking and bring to a boil. Reduce heat to low and reduce sauce until thicker (about 7 minutes).
3. Add gruyere 3 oz
4. Add salt, pepper, and nutmeg.
5. Meanwhile, butter bread and place onto a griddle to toast. Flip after 3 minutes to toast the other side.
6. After bread is flipped add 2 slices of gruyere to each toast
7. Add ham to one side and top with other toast
8. Allow to cook for 3-4 minutes until cheese is melted
9. Top with Mornay sauce and sprinkle extra Gruyere & broil for less than a minute
10. Crack eggs onto skillet or griddle and cook to sunny side up (can do more if desired).
11. Remove from broiler and top each sandwich with 2 eggs. Serve immediately.