Heat oven to 350 degrees F.

Line 8 indentations of one or two jumbo muffin tins with paper or foil liners.

In a medium bowl, whisk together the flour, baking soda, baking powder, cinnamon, salt, cloves, allspice and freshly grated nutmeg. Set aside.

Pour oil into a large bowl. Crumble brown sugar into oil, breaking up any lumps with hands. Beat together with an electric mixer until combined. Add the eggs, one at a time, and beat until well blended. Stir in the flour mixture until no lumps remain. Fold in shredded carrot and walnuts until combined. Transfer batter to prepared muffin tins, a scant 2/3 cup per indentation.

Bake in 350 degrees F oven for 30 minutes, or until tops have crowned and toothpick inserted in centers comes out clean.

Place muffin tins on wire rack and cool cupcakes in tins about 5 minutes, then turn out and cool completely on a wire rack. Reline pan and repeat with remaining batter if necessary.

While cupcakes cool, prepare Icing: In a medium bowl with an electric mixer on low speed, beat together the cream cheese, confectioners' sugar, heavy cream and vanilla extract. Refrigerate until time to ice.

When ready to ice cupcakes, set aside 1/2 cup icing. Spread remaining icing onto cupcakes, a scant 1/4 cup per cupcake.

Tint 1/4 cup of the reserved icing green. To tint remaining 1/4 cup icing orange, add a few drops each of yellow and red coloring until desired intensity is reached.

Transfer colored icings to 2 small plastic heavy duty food storage bags. Snip off a small corner of the bags and use to pipe carrots on top of cupcakes, if desired. (It helps if you practice making the carrot design first on waxed paper.)