Mash strawberries with 1/2 cup sugar; cover and chill overnight.
Combine remaining sugar, cornstarch, and salt in a large Dutch oven; gradually stir in milk. Cook over medium heat, stirring constantly with a metal spoon, 10 minutes or until slightly thickened.
Beat 3 eggs and egg yolks. Stir one-fourth of hot milk mixture into beaten eggs; add to remaining hot milk mixture, stirring constantly. Cook over medium heat 2 minutes or until mixture coats the spoon. Cool to room temperature; chill several hours. Stir in vanilla.
Fold strawberries into chilled custard mixture; stir well. Pour mixture into freezer can of a 5- quart hand-turned or electric freezer. Freeze according to manufacturer's instructions. Let ripen 1 1/2 to 2 hours before serving. Scoop into individual bowls, and serve immediately.