Pre-heat the oven to 450 degrees.
Place the grapes on a baking sheet and drizzle with the olive oil. Add a pinch of salt and a little fresh ground pepper and toss to coat. Roast for 15 minutes, tossing halfway through the cooking time, until the grapes have softened and the skins are lightly browned in spots. Let cool slightly.
Meanwhile make the dressing. Place all the ingredients for the dressing in a small food processor or blender (a Nutribullet or one of those little ninja blenders will do the trick). Add a pinch of salt and pepper and process until smooth. (If you don’t have a small processor/blender, you can grate the garlic, mince the shallot, and whisk it with the other ingredients for the dressing except the basil. Simply chop the basil and toss it with the lettuce.)
Place the lettuce in a mixing bowl. Add the chicken, roasted grapes, and celery, and toss gently to combine. Dive the mixture between to large plates or bowls. Top each salad with cheese and pistachios. Drizzle each salad generously with the desired amount of dressing and serve.