Step 1Trim the stem ends of the berries so they will be the same height when placed in the bottom of the pie plate. Set aside.
Step 2Whip the goat cheese in a mixer or food processor until light. Remove to a bowl, add the milk and beat to blend. Add the tarragon and stir to mix.
Step 3Spread the cheese mixture evenly in the bottom of the pie crust. Arrange the whole berries, pointed side up, on the goat cheese, covering the entire surface of the pie. Set aside.
Step 4In a medium saucepan, combine the sugar, cornstarch, lemon zest, water and balsamic vinegar. Bring to a boil over medium heat, then add the sliced strawberries and continue to cook until thickened, about 5 to 7 minutes. Pour the hot glaze-strawberry mixture over the whole strawberries. Refrigerate until the glaze sets, about 4 to 6 hours.