1. Whisk together sugar and cocoa in a medium bowl. Combine coffee and vanilla.
2. Beat butter at medium speed with a heavy-duty electric stand mixer until creamy; gradually add sugar mixture alternately with coffee mixture, beating at low speed until blended. Beat in half-and-half, 1 Tbsp. at a time, until smooth and mixture has reached desired consistency.
Mocha-Almond Frosting: Decrease vanilla extract to 1 tsp. Proceed with recipe as directed, adding 1/2 tsp. almond extract to coffee mixture in Step 1.