Preheat oven to 350°. Spread pistachios on a large baking sheet and bake until very lightly toasted (they should still retain some green), 8 to 10 minutes. Remove from oven and cool to room temperature.
In a large bowl, toss together lettuce, tarragon, mint, and half of the strawberries. In a small bowl, whisk together lemon juice, shallot, honey, and salt. Drizzle in olive oil, whisking constantly, until mixture is emulsified. Drizzle dressing over lettuce mixture and toss well.
Divide lettuce mixture among plates, then top with remaining strawberries, toasted pistachios, and feta triangles.
Note: Nutritional analysis is per first-course serving.