2 - 3 zucchini (about 1 lb.)
Kosher salt
2 tbsp. plus 1 tsp. extra-virgin olive oil
1 tbsp. balsamic vinegar
1/2 tsp. chopped fresh thyme
1/2 tsp. finely grated lemon zest
Fresh ground black pepper
3 tbsp. grated Parmesan Cheese

Wash the zucchini well to remove any grit and dry them with paper towels; trim off the ends. Quarter each zucchini lengthwise, then slice off the top 1/4 to 1/2 inch of the soft seed core by running a sharp knife down the length of each quarter; it's fine if some of the seeds remain. Arrange the zucchini, cut side up, on a baking sheet lined with paper towels. Sprinkle with salt (about 1/2 tsp. per 1 lb. of zucchini) and set aside for 10 minutes. Blot the quarters dry with paper towels.

Heat a gas grill to medium high or prepare a medium-hot charcoal fire.

In a small bowl, whisk 2 tablespoons of the oil, the vinegar, thyme, lemon zest, 1 teaspoon salt, and 1 teaspoon pepper.

Toss the zucchini with the remaining 1 teaspoon olive oil, Set the zucchini cut side down on the grill and cook (it using a gas grill, keep the lid closed), flipping occasionally, until it browns and softens but doesn't turn mushy, 6 to 8 minutes. Cut the zucchini into 3-inch pieces and put in a medium bowl.

Whisk the vinaigrette again and drizzle over the zucchini. Sprinkle on the Parmesan, toss well, and adjust the seasonings to taste. Serve immediately.