In Martha's grown-up take on the beloved ice cream flavor, ripe strawberries are pureed for the base, then macerated with vodka or tequila and folded in after churning.
In a blender, puree halved strawberries with lemon juice and salt. Strain through a fine-mesh sieve. (You should have 1 1/2 cups of puree; reserve any excess for another use.)
Combine milk, cream, 2/3 cup sugar, and corn syrup in a medium saucepan. Bring to a boil, then reduce heat to low and simmer 2 minutes. Strain mixture into a bowl set in an ice bath and let stand, stirring occasionally, until cold, about 5 minutes. Stir in strawberry puree. Refrigerate, covered, at least 2 hours and up to overnight.
Stir together remaining 1/2 cup sugar and vodka. Add chopped strawberries and macerate at room temperature at least 2 hours, or in the refrigerator, covered, up to 12 hours.
Process puree mixture in an ice cream maker according to manufacturer's instructions. When it has the texture of soft serve, drain macerated berries (reserving syrup for another use) and fold into ice cream. Transfer to a loaf pan and freeze, wrapped in plastic, at least 4 hours and up to 1 week. Let stand at room temperature 10 minutes before serving.