For Carrot Cake: Preheat oven to 350. Butter and flour 12 cup Bundt pan. Cook carrots in pot of boiling water until tender, about 15 min. Drain well. Transfer cooked carrots to food processor and puree. Transfer 1 1/2 cups puree to small bowl (save any remaing puree for another use). Add milk to carrot puree; stir to combine.
Whisk flour, cinnamon, baking powder and baking soda in medium bowl to blend. Using electric mixer, beat sugar, butter and salt in large bowl to blend. Add eggs to butter mixture one at a time, beating well after each addition. Beat in vanila extract. Beat in flour mixture alternately with carrot mixture in 3 addions each. Fold in toasted walnuts, 1 cup coconut and apricots. Transfer batter to prepared pan.
Bake cake until tester inserted near center comes out clean, about 55 min. Cool cake in pan on rack 20 min. Invert cake onto rack.
Orange Glaze: Whisk powdered sugar, orange juice and peel in small bowl to blend. Pour glaze over wark cake. Sprinkle remaining 2 tbs. shredded coconut over glaze. Cool. Cake can be prepared 2 days ahead; Store airtight at room temperature.
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