Fry turkey bacon according to package instructions.
Crack egg in a shallow dish, add milk and whisk till combined.
Spread mustard on all slices of bread.
Layer between the bread: roasted turkey, turkey bacon, cheese, then arugula.
Heat a medium size frying pan to medium heat.
Dip layered sandwich in egg mixture (both sides).
Add butter to plan, melt, then place sandwich in frying pan and cook on one side until golden brown (about 5 minutes).
Flip and cook on the other side until golden brown (about 5 minutes).
Remove from pan, slice, and serve hot.