Coat a 9-inch round cake pan with cooking spray. Line bottom of pan with parchment paper; coat with cooking spray. Dust with 2 teaspoons flour.
Reserve 5 walnuts. Place remaining walnuts, 6 dates, and clementines in food processor; process until ground.
Combine brown sugar, butter, and oil in a large bowl; beat with a mixer at medium speed until well blended. Beat in vanilla and egg.
Combine flour, baking soda, and salt. Add flour mixture and buttermilk alternately to sugar mixture, beginning and ending with flour mixture; mix after each addition. Add nut mixture and chopped dates; beat at medium speed 3 minutes. Pour batter into prepared pan. Bake at 350° for 45 minutes or until a wooden pick inserted in center comes out clean. Cool in pan 10 minutes on a wire rack; remove from pan.
Combine powdered sugar and juice, stirring with a whisk until smooth. Drizzle glaze over warm cake; spread to coat top. Top with reserved 5 walnut halves. Cool cake on a wire rack 30 minutes.