Heat oven to 350°F. Let cookie dough stand at room temperature 10 minutes to soften. Spray 32 mini muffin cups with Crisco® No-Stick Cooking Spray with Flour.
In large bowl, beat cookie dough, melted butter, 1 tablespoon molasses, 2 tablespoons milk, ginger, 1 1/2 teaspoons cinnamon, and nutmeg with electric mixer on medium speed until blended. Add carrots and pecans; beat on low speed just until blended. Spoon 1 heaping tablespoonful batter into each muffin cup.
Bake 16 to 21 minutes or until toothpick inserted in center comes out clean. Cool in pan 10 minutes; remove from pans to cooling racks. Cool completely, about 30 minutes.
To make frosting, in large bowl, beat 7 tablespoons butter and 1 tablespoon molasses with electric mixer on medium speed until creamy. Add powdered sugar, 1/2 teaspoon cinnamon and 2 tablespoons milk, beat on medium speed until smooth. Spread or pipe frosting onto cupcakes. Store in covered container.