Prepare the flavored vinegar by mashing three strawberries against the side of a small bowl with a fork.
Add 4 cup of good-quality balsamic vinegar and stir to combine.
Set this aside at room temperature to allow the vinegar to absorb the strawberry flavor, 1 to 2 hours.
Strain the flavored vinegar through a sieve, pressing to release all the liquid from the berries. Discard the solids and set the strawberry vinegar aside.
Meanwhile, cut the remaining strawberries in half lengthwise so they are bite-size. Place the berries in a small, shallow bowl, add the 2 tablespoons of aged balsamic vinegar, and stir to coat.
Set the berries aside to marinate at room temperature, 1 to 2 hours, stirring occasionally.
Prepare the vinaigrette by placing the strawberry-flavored vinegar, olive oil, mustard, and salt in a glass jar and tightly close the lid. Shake the jar vigorously to combine. Taste and adjust the seasonings to taste.
Just before serving, place the mixed greens and tarragon in a large salad bowl and toss to combine. Add 3 tablespoons of the vinaigrette. Toss to lightly coat the leaves and taste them to see if more vinaigrette is needed. (Leftover dressing can be stored, covered, in the refrigerator, for up to 3 days.).
Transfer the greens to individual salad plates. Arrange the marinated strawberries on the greens and sprinkle them with the nuts and cheese. Serve immediately.