Peppermint Ice Cream Candyland Cake

Ingredients:
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
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)
1/2 cup water
8 ounces bittersweet or semisweet chocolate chips

Instructions:
Preheat oven to 350°F. Butter 15x10x1-inch baking sheet; line with parchment. Butter parchment. Whisk first 4 ingredients in large bowl. Melt butter in medium saucepan. Remove from heat. Add chocolate chips; stir until melted. Whisk in 3/4 cup water, cocoa, and vanilla until blended. Whisk in egg. Add to dry ingredients; whisk to blend. Pour batter onto prepared baking sheet.
Bake cake until tester inserted into center comes out with some moist crumbs attached, about 22 minutes. Cool cake on baking sheet on rack 15 minutes. Run knife around pan sides to loosen cake. Turn cake out onto sheet of foil; cool. Cut cake crosswise into 3 equal strips. Freeze cake strips 1 hour.
Place 1 cake strip on platter. Working quickly, spoon 3 1/2 cups peppermint ice cream in dollops over cake; spread evenly to edges. Top with second cake strip; spoon 3 1/2 cups ice cream in dollops over cake; spread evenly to edges. Top with third cake strip; freeze 1 hour. Spread enough remaining ice cream over top and sides of cake to cover generously (about 6 cups). Freeze until firm, about 3 hours.
Place 20-inch-long sheet of foil on work surface. Mark off 16x12-inch rectangle. Stir sugar, 1/2 cup water, and corn syrup in heavy small saucepan over medium-low heat until sugar dissolves, brushing down sides of pan with wet pastry brush. Increase heat and boil without stirring until candy thermometer registers 300°F, tilting saucepan slightly to submerge bulb, about 15 minutes.
Being very careful (syrup is extremely hot), pour boiling syrup in wide zigzag lines across foil. Working quickly and using offset metal spatula, spread syrup evenly to 16x12-inch rectangle. Immediately sprinkle generously with candies, pressing larger pieces into syrup to adhere (do not touch hot syrup). If syrup hardens before all candies have been applied, slide foil with brittle onto large rimless baking sheet and place baking sheet directly over burner set on high heat to soften syrup, about 10 seconds, rotating sheet, then remove from heat and immediately apply remaining candies. Cool completely.
Starting at 1 end of brittle, break off irregular pieces, peeling foil as you go. Press brittle upright, candy side out, onto top and sides of cake and freeze. DO AHEAD: Cake can be made 2 days ahead. Cover and keep frozen.
Bring water to simmer in small saucepan. Remove from heat. Add chocolate; whisk until smooth. DO AHEAD: Sauce can be made 2 days ahead. Cover and chill. Rewarm sauce before continuing.
Slice cake and serve with sauce.