Grease and lightly flour three 9 x 1 1/2-inch round baking pans; set aside.
In a covered medium saucepan cook carrots in a moderate amount of boiling water about 20 minutes or until very tender; drain.
Cool carrots slightly. Coarsely mash with a potato masher.
In a very large bowl stir together flour, sugar, cinnamon, baking powder, baking soda and salt.
Make a well in center of flour mixture. Add vegetable oil, eggs, pineapple and vanilla extract. Beat with an electric mixer on low speed until all ingredients are combined. Fold in mashed carrots, pecans and coconut.
Spread batter evenly in prepared pan.
Bake in a preheated 350 degree F. oven 35 - 40 minutes or until a wooden pick inserted in centers comes out clean.
Cool in pans on wire racks 10 minutes. Remove from pans. Cool completely on racks. While layers are cooling, prepare cream cheese frosting.
Cream Cheese Frosting:
Cream butter and sugar until fluffy. Add cream cheese and vanilla extract; beat until fluffy. Stir in chopped pecans.
Use pecan halves for garnish if desired.
In small saucepan melt butter over medium heat. Stir in brown sugar and whipping cream. Bring to full boil, stirring constantly. Reduce heat.