1. In a 3-quart saucepan, whisk together sugar and cocoa until well blended. Pour in half-and-half cream, and bring to a boil over high heat, whisking gently but constantly.
2. In a medium bowl, whisk together egg yolks and salt. Pour 1 cup of the hot half-and-half mixture into the egg yolks, beating with a wire whisk the whole time. Pour this mixture back into the saucepan with the half-and-half mixture, stirring constantly. Cook over medium heat, about 1 minute, stirring constantly with a rubber spatula just until the mixture thickens a little bit and lightly coats the back of the spatula. Do not let mixture come to a boil. Remove from heat and stir in heavy cream and vanilla.
3. Pour mixture into a 9x13-inch baking pan. Let stand 10 minutes to cool.
4. Freeze uncovered, 1 hour. Scrape sides of pan and stir. Freeze 1 hour more. Remove ice cream from freezer, scrape sides of pan again, and beat ice cream with an electric mixer briefly to break up ice crystals. Return ice cream to freeze until it is almost completely set, about 1 hour more. Remove ice cream from freezer, and beat with electric mixer once more. Cover with plastic wrap, and keep in freezer until ready to serve. Makes 6 cups.