3/4 cup granulated sugar
1/4 cup vegetable oil
1 tablespoon orange juice
2 teaspoons grated orange peel
1-1/2 teaspoons vanilla extract
2 cups all-purpose flour
1/2 cup finely chopped walnuts
1 teaspoon baking powder
1/4 teaspoon salt
1 cup chopped dried tart cherries
1 egg white
1 tablespoon water
Combine 3/4 cup sugar and eggs in a large mixing bowl. Beat with an electric mixer at medium speed, scraping bowl often, 2 to 3 minutes, or until thick and pale yellow in color. Add oil, orange juice, orange peel and vanilla; beat 1 to 2 minutes, or until well mixed. Combine flour, walnuts, baking powder and salt; gradually add to egg mixture. Mix on low speed 1 to 2 minutes, or until well mixed. Stir in cherries by hand.
Turn dough onto lightly floured surface (dough will be soft and sticky). Lightly sprinkle with additional flour; knead flour into dough. With floured hands, shape into 2 (8×2-inch) logs. Place 3 to 4 inches apart on a greased baking sheet; flatten tops slightly. Combine egg white and water; brush on logs. Sprinkle with granulated sugar.
Bake in a preheated 350-degree oven 25 to 30 minutes, or until light brown and firm to the touch. Let cool on baking sheet 15 minutes.
Reduce oven temperature to 300 degrees. Cut logs diagonally into 1/2-inch slices with a serrated knife; arrange slices, cut-side down, on baking sheet. Bake 8 to 10 minutes; turn slices. Bake 8 to 10 minutes, or until golden brown. Remove to wire rack; let cool completely.