In a large saucepan stir together sugar, flour, and salt. Stir in milk and eggs. Bring just to boiling over medium heat, stirring frequently. Reduce heat; cook and stir for 1 minute more. Remove from heat.
Whisk in melted chocolate until combined. Whisk in whipping cream and vanilla. Transfer chocolate mixture to a large bowl. Cover surface of mixture with plastic wrap. Chill for 8 to 24 hours. (Or to chill quickly, place bowl in a sink of ice water for 30 to 60 minutes, stirring occasionally.)
Freeze mixture in a 4- to 5-quart ice cream freezer according to the manufacturer's directions. To ripen, transfer to a pan or freezer container. Cover and store in the freezer for at least 4 hours or until firm.