1. Preheat oven to 325°. Beat butter and 1 1/2 cups sugar at medium speed with a heavy-duty electric stand mixer 4 to 5 minutes or until creamy. Add eggs, 1 at a time, beating just until blended after each addition. Beat in vanilla extract.
2. Sift together flour, baking powder, and salt. Add to butter mixture alternately with half-and-half, beginning and ending with flour mixture. Beat at low speed just until blended after each addition, stopping to scrape bowl as needed.
3. Spoon 1 1/4 cups batter into a 2-qt. bowl, and stir in cocoa, 3 Tbsp. hot water, and remaining 1/4 cup sugar until well blended.
4. Spread remaining vanilla batter into a greased and floured 15- x 10-inch jelly-roll pan. Spoon chocolate batter onto vanilla batter in pan; gently swirl with a knife or small spatula.
5. Bake at 325° for 23 to 28 minutes or until a wooden pick inserted in center comes out clean. Cool completely in pan on a wire rack (about 1 hour). Spread top of cake with Mocha Frosting.