Cake:
1 1/2 cups unbleached all purpose flour
1 1/2 cups sugar
3/4 teaspoon baking soda
1/4 teaspoon salt
3/4 cup (1 1/2 sticks) unsalted butter
6 tablespoons bittersweet or semisweet chocolate chips
3/4 cup water
1/2 cup unsweetened cocoa powder
1 1/2 teaspoons vanilla extract
1 large egg, room temperature
3 1/2 quarts (about) peppermint stick ice cream, slightly softened

Candy Brittle:
1 1/2 cups sugar
1/2 cup water
1 1/2 tablespoons light corn syrup
1 to 2 cups assorted candies (such as sliced gummy candies, spice drops, Swedish mints, butter mints, rock candy pieces, and candy cane pieces)

Chocolate Sauce:
1/2 cup water
8 ounces bittersweet or semisweet chocolate chips