Preheat oven to 350°F. Grease a 13 ×9-inch baking pan. In a medium bowl stir together first six ingredients (through nutmeg). In a large bowl combine remaining five ingredients (through vegetable oil); whisk until smooth. Add flour mixture to pumpkin mixture, one-third at a time, stirring after each addition just until combined.

Spread batter into prepared pan. Break cookie dough into 3/4-inch chunks. Arrange cookie dough chunks evenly over batter. Gently poke the pieces halfway down into batter. Bake until a toothpick comes out clean, 30 to 40 minutes. Cool cake completely in pan on a wire rack.

Meanwhile, for frosting, in a large bowl beat butter with a mixer on medium until creamy, 1 to 2 minutes. Beat in 1/2 cup of the powdered sugar. Add 2 Tbsp. of the cream, the vanilla, and salt; beat on low until combined. Gradually beat in remaining 11/2 cups powdered sugar and the cocoa just until combined. Beat on medium, scraping bowl occasionally, until fluffy, 5 minutes. Add remaining 1 Tbsp. cream; beat on high 1 minute more. 

Spread frosting over cooled cake. If you like, top each piece with a mini chocolate chip cookie.