Grilled Delicata Squash with Mizuna, Pecorino and Pinenut Salad

1 medium delicate squash, sliced into 1/2" thick disks or quartered, lengthwise
Olive oil, for brushing squash
Kosher salt and freshly ground black pepper
3 cups mizuna leaves, loosely packed
2 tablespoons juice from 1 to 2 lemons
3 tablespoons extra virgin olive oil
2 ounces pecorino or parmesan cheese, shaved into thin slices using a vegetable peeler
2 tablespoons toasted pinenuts
Procedures
1 Light one chimney full of charcoal. When all the charcoal is lit and covered with gray ash, pour out and spread the coals evenly over the coal grate. Set cooking grate in place, cover grill and allow to preheat for 5 minutes. Alternatively, preheat a gas grill to high, covered, for at least 10 minutes. Clean and oil the grilling grate.
2 Using a pastry brush, brush squash with olive oil on both sides, and season to taste with salt and pepper.
3 When grill is hot, add squash slices and cook, covered, until squash is well-browned on one side, 4 to 5 minutes. Flip slices and cook, covered, until zucchini is well-browned and tender, 3 to 4 minutes. Transfer squash to a serving platter.
4 In a medium bowl, toss mizuna with lemon juice, extra virgin olive oil, and salt and pepper to taste. Gently mound salad on top of grilled zucchini. Garnish with cheese and pinenuts and serve