Step 1

Preheat oven to 350°F. Line 10 standard (1/3-cup) muffin cups with paper liners. Combine butter, 1/2 cup chocolate chips, and unsweetened chocolate in top of double boiler set over simmering water. Stir until mixture is melted and smooth. Remove from over water. Whisk both sugars into chocolate mixture, then whisk in eggs 1 at a time. Whisk in vanilla, then flour, walnuts, salt, and remaining 3/4 cup chocolate chips. Divide batter among prepared muffin cups (about 1/4 cup for each). Bake cupcakes until tester inserted into center comes out with moist crumbs attached, about 20 minutes. Transfer cupcakes to rack and cool completely.

Step 2

Put powdered sugar and next 3 ingredients in medium bowl. Using electric mixer, beat until mixture is smooth, adding whipping cream by teaspoonfuls if frosting is too thick to spread.

Step 3

Spread frosting in swirls over top of cupcakes. Sprinkle with chocolate shavings or chocolate sprinkles. DO AHEAD Can be made 1 day ahead. Store in single layer in airtight container at room temperature.