Preheat oven to 350°. In a large bowl, beat sugar, oil, honey and egg until well blended. In another bowl, whisk flour, baking soda, cinnamon and salt; gradually beat into sugar mixture. Stir in 1 cup walnuts.
Spread into a greased 15x10x1-in. baking pan. Bake until golden brown (edges will puff up), 10-12 minutes. Cool completely on a wire rack.
For glaze, in a small bowl, mix confectioners' sugar, mayonnaise, vanilla and enough water to reach desired consistency; spread over top. If desired, sprinkle with additional walnuts. Let stand until set. Cut into bars. Refrigerate leftovers.