In a large skillet, melt 2 tablespoons of butter over medium heat.
Add maple syrup and brown sugar, stirring to dissolve.
Add salmon to the pan and toss to coat with the glaze; continue cooking approximately 5-6 minutes, until the glaze reduces and becomes thick; stir occasionally.
In another skillet coated with non-stick cooking spray, crack eggs into pan, careful not to break the yolks, and cook over medium-high heat until whites are opaque (approximately 1-2 minutes).
Flip eggs over to cook through for approximately 1 more minute.
Place smoked salmon mixture on half of a roll, top with egg and cover with top of roll; repeat for second sandwich and serve.