In medium pot, combine strawberries, lemon juice, and ⅓ cup sugar over medium heat and bring to boil
Reduce heat and simmer for 25 minutes
Remove from heat, press through sieve, reserving syrup
Set aside for later to cool
Mix on low speed ¾ cup sugar and milk in a large glass bowl
Once sugar has dissolved, gently stir in cream and vanilla, then pour immediately into ice cream machine
Chop up packet of cookies and add to machine in last 5 minutes
Melt chocolate and oil over double boiler until smooth, cool slightly
Freeze ice cream for 1 hour, pour chocolate over and freeze for three more hours before serving.