In a heavy saucepan, combine the sugar, flour and salt. Gradually add milk until smooth. Bring to a boil over medium heat; cook and stir for 2 minutes or until thickened. Remove from the heat; cool slightly.
Whisk a small amount of hot milk mixture into the eggs; return all to the pan, whisking constantly. Cook and stir over low heat until mixture reaches at least 160� and coats the back of a metal spoon. Stir in the cream cheese until melted.
Remove from the heat. Cool quickly by placing pan in a bowl of ice water; stir for 2 minutes. Stir in vanilla. Press plastic wrap onto surface of custard. Refrigerate for several hours or overnight.
Stir strawberries and cream into custard. Fill cylinder of ice cream freezer two-thirds full; freeze according to the manufacturer's directions. Refrigerate remaining mixture until ready to freeze. Allow to ripen in ice cream freezer or firm up in the refrigerator freezer for 2-4 hours before serving. Yield: 1 gallon.