Preheat oven to 350 degrees, with racks in upper and lower thirds. In a medium bowl, whisk together flour and salt. In a large bowl, using an electric mixer, beat butter and sugar until light and fluffy. Beat in 1/2 cup maple syrup and egg yolks. With mixer on low, beat in flour mixture.
Drop batter by tablespoons, 3 inches apart, onto two baking sheets. Using a flat-bottomed glass dipped in flour, flatten cookies to a 1/4-inch thickness. Bake until golden at edges, 12 to 15 minutes, rotating sheets halfway through. Transfer cookies to wire racks to cool. In a small saucepan, simmer 1 cup maple syrup until reduced to 3/4 cup. Spoon over cookies.