Preheat oven to 350°.
To prepare brownies, place 1/2 ounce chocolate in a microwave-safe dish, and microwave at high 30 seconds or until almost melted, stirring once. Combine chocolate, 1/2 cup sugar, and butter in a medium bowl; beat with a mixer at high speed until well blended. Add extract and egg; beat until combined. Lightly spoon flour into a dry measuring cup; level with a knife. Combine flour, 1/3 cup cocoa, baking powder, and salt. Add flour mixture to sugar mixture; beat just until blended. Spoon batter into a 9 x 5-inch loaf pan coated with cooking spray. Bake at 350° for 20 minutes or until a wooden pick inserted in the center comes out clean. Cool in pan on a wire rack.
To prepare ice cream, combine 1 1/3 cups sugar and 1/3 cup cocoa in a medium, heavy saucepan over medium-low heat, stirring well with a whisk. Stir in 1/2 cup milk and egg yolks. Stir in remaining 3 cups milk. Cook 12 minutes or until a thermometer registers 160°, stirring constantly. Remove from heat.
Place half-and-half in a medium microwave-safe bowl; microwave at high 1 1/2 minutes or until half-and-half boils. Add 2 1/2 ounces chocolate; stir until smooth. Stir half-and-half mixture into milk mixture. Place pan in a large ice-filled bowl. Cool completely, stirring occasionally.
Pour mixture into the freezer can of an ice-cream freezer; freeze according to manufacturer's instructions. Spoon ice cream into a freezer-safe container. Cut brownies into small squares; stir into ice cream. Cover and freeze 1 hour or until firm.