In a medium bowl, whisk together flour, 3/4 cup cornmeal, baking powder and salt. Set aside. On medium speed, use an electric mixer to beat the butter, sugar and egg until creamy, scraping the bowl often for about two minutes. Reduce the speed to low, add the flour mixture, zest and orange extract then beat until the mixture pulls away from the sides and forms dough, about one minute. Divide the mixture in half and form each half into 12 inch long, 1 1/2 inch wide log. Cover with plastic wrap and chill until firm, about one hour in the refrigerator or 20 minutes in the freezer. Heat oven to 375 degrees. Line two rimmed cookie sheets with parchment paper. Spread the remaining 1/4 cup of cornmeal on a small flat tray. Roll each log in the cornmeal to coat. Cut the logs into 1/2 inch thick slices and place them one inch a part on the cookie sheets. Bake until the cookies are deep golden brown around the edges, about 10-12 minutes, rotating the sheets halfway through. Cool the trays for about 5 minutes then transfer them to a cooling rack.
To make the glaze, stir together confectioners sugar, zest, 1/4 cup orange juice and salt. If needed, add more juice, a teaspoon at a time, until the glaze has a flowing consistency. Spoon a few teaspoons of the glaze onto each cookie.