Preheat oven to 350 degrees. Prepare a 9"x13" baking pan with baking spray.
In a large mixer bowl, beat butter and sugar together until light and fluffy, about 4 minutes.
Add salt and larger portion of eggs (reserving 1 tablespoon for egg wash) to butter mixture. Beat well.
Gradually add in the flour. Mix well, but do not overbeat. Stir in gingers and rosemary.
Press dough evenly into baking pan.
In small bowl combine milk and 1 tablespoon of egg. Beat well. Using a pastry brush, lightly brush top of shortbread.
Bake for 35-40 minutes, or until a tester comes out clean. Cool in pan on wire rack.
When shortbread is cool, transfer to a large cutting board. The sides of the shortbread may be very dark. You can trim the edges with a large knife if needed.
With long side of shortbread facing you, cut into seven equal strips. Cut each strip into 5 equal squares. Cut each square diagonally into two triangles.
Store shortbread in an airtight container, or freeze with waxed paper, or parchment, between layers.