Place strawberries in medium-size bowl. Combine 1/2 cup of sugar and water in medium-size saucepan. Bring to boiling, swirling pan until sugar is dissolved. Pour over strawberries, tossing to combine. Refrigerate.
Combine remaining sugar and cornstarch in dish. Combine milk and cornstarch mixture in saucepan. Cook over medium heat until bubbly and thickened, whisking constantly. Remove from heat. Stir in half-and-half. Chill in freezer 15 minutes.
Strain syrup from strawberries into milk mixture. Freeze in ice-cream freezer, according to manufacturers directions. Stir in strawberries, pistachios and vanilla until blended. Pack in airtight container. Freeze at least 2 hours or overnight.
Spoon into sundae dishes. Serve with strawberry sauce and whipped cream, if you wish. Makes 5-1/2 cups.