Preparation

Slice and salt the zucchini:

• Wash the zucchini well to remove any grit and dry them with paper towels. Trim off the ends and quarter the zucchini lengthwise. 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 all right if some of the seeds remain. Arrange the zucchini, cut side up, on a baking sheet lined with paper towels. Sprinkle with kosher salt (about 1/2 tsp. per 1 lb. of zucchini) and set aside for 10 min. Blot the quarters dry with the paper towels.

Assemble and cook the dish:

• Heat a gas grill to medium high or prepare a medium-hot charcoal fire. In a small bowl, whisk 2 Tbs. of the oil, the vinegar, thyme, lemon zest, 1/4 tsp. salt, and 1/8 tsp. pepper.
• Toss the zucchini with the remaining 1 tsp. olive oil. Set the zucchini cut side down on the grill and cook (if using a gas grill, keep the lid closed), flipping occasionally, until it browns and softens but doesn’t turn mushy, 6 to 8 min. 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 Parmigiano, toss well, adjust the seasonings to taste, and serve immediately.