Place 14 of the strawberries in the freezer for 2 hours. They will act as your "ice cubes" in the cocktail. (This can be done well ahead of time.)
Add the remaining 6 strawberries, 2 ounces of lemonade, and the mint leaves to a blender. Cover and puree until smooth. (You should have about 4 ounces. If not, add more lemonade as needed.)
Divide the frozen strawberries between two Collins glasses. Set aside.
Fill a cocktail shaker with ice. Add the Pimm's liqueur, the strawberry puree, and 8 ounces of lemonade. Cover and shake vigorously until chilled.
Divide between the two glasses over the frozen strawberries and garnish with fresh mint.