Melt butter over low heat. Remove from heat and add 2 cups of the flour and the sugar. Beat in the eggs one at a time until well blended. Slowly mix in the remaining 2 cups of flour.
Roll out the dough on a floured surface to a thickness of 1/4 of an inch. Cut cookies using cookie cutters and place 1 1/2 inches apart on cookie sheets.
Bake in preheated oven until cookies are light brown at the edges, 12 to 15 minutes (depending on their size).
