To make the strawberry syrup: Bring syrup ingredients (strawberries - salt) to a boil in a saucepan over medium high heat, stirring until sugar dissolves. Boil uncovered 10 minutes on low, stirring occasionally. Add the lemon juice. Strain, pressing down on the solids.
Cover and chill for at least one hour or up to one week.
Place 2 (12 - ounce) glasses in the freezer for one hour. (The original recipe made 4 glasses but used 2 pints of ice cream).
To make the milk shakes: place 1 cup strawberry syrup, 1 cup milk, and 1 cup ice cream in a blender and puree until smooth. (For four glasses just use 1 pint of ice cream.) Add second cup of ice cream (or for 4 glasses use 2 cups of ice cream) and puree until almost smooth.
Pour into frozen glasses. Drizzle with additional strawberry syrup if desired and garnish with strawberries if desired.