Puree the strawberries using a blender or food processor. Push the puree through a fine mesh sieve sitting over a bowl to remove the strawberry seeds.
Place strained puree into a small saucepan over medium heat. Add the sugar and mix well.
Bring to a simmer and simmer for about 5 minutes or until the puree is reduced by about a third.
While puree is simmering, add ¼ cup of water to a small bowl. Sprinkle the gelatin over the water evenly. Set aside.
Once the puree has reduced by a third, add the gelatin, stirring well.
Bring the puree back to a gentle boil for about 2 minutes.
Remove the saucepan from the heat and stir in the balsamic vinegar. Pour the puree into a small bowl and allow to cool for about 20-25 minutes.
Using a stand mixer or bowl and hand mixer, whip the heavy cream to stiff peaks.
Fold the cooled strawberry puree gently into the whipped cream until completely incorporated.
Remove the pie crust from the refrigerator and fill with the strawberry mousse, using a spatula to smooth out the top.
Refrigerate for at least 2 hours or overnight. If desired, top with strawberries and/or whipped cream.