In a large bowl, toss together the plums, 1 tablespoon olive oil and 1/4 teaspoon salt. Place the plum wedges on the hot grill pan and grill until nice grill marks have formed, 1 to 2 minutes per side. Remove to a plate to cool slightly.
To the large bowl add the lettuce, basil, mint, white balsamic vinegar, remaining 1 tablespoon olive oil, and remaining 1/4 teaspoon salt. Using your hands, gently toss to coat the greens, being careful not to bruise the lettuce. Sprinkle the salad with the pistachios and gently place the plums on top. Sprinkle with the ricotta shavings and serve.