Can’t find white balsamic vinegar? Use regular balsamic or white wine vinegar.
Stir together diced strawberries, shallot, vinegar, honey, salt and pepper in a large bowl. Let stand 15 minutes. Slightly mash with a whisk. Whisk in oil and tarragon; reserve 2 tablespoons of the dressing mixture.
Add lettuces and quartered strawberries to dressing mixture; toss to combine. Transfer to a platter or individual plates; top with avocado slices and pine nuts. Drizzle with reserved dressing.