In a blender, combine the 1 pound strawberries with the strawberry jam, agave, and lemon juice. Blend until smooth, 20 to 30 seconds, then transfer to a container. (The strawberry sauce can be made ahead of time and stored in the refrigerator for up to 5 days.)
In the blender, combine 1 cup of the strawberry sauce with the milk, cream cheese, ice cream and the remaining 4 strawberries. Blend on high speed until smooth.
For each serving, add 1/4 cup of the remaining strawberry sauce to a 12-ounce glass; swirl the sauce around base of glass. Fill to the top with the ice cream mixture. Drink immediately.