Preheat grill to medium (350°F to 400°F). Cut larger squash into 1-inch-thick slices; leave any smaller squash whole. Place squash, mint, salt, 2 tablespoons of the oil, and 1/4 teaspoon of the pepper in a small bowl; toss to coat. Let stand 20 minutes.
Meanwhile, stir together vinegar, shallot, honey, mustard, 1/4 cup of the feta, and remaining 1/4 teaspoon pepper in a small bowl. Gradually whisk in remaining 1/2 cup oil.
Grill squash until slightly charred and tender, about 5 minutes per side. Transfer squash to a serving platter; drizzle with 3 tablespoons of the vinegar dressing. Sprinkle with parsley and remaining 1/4 cup feta. Serve immediately with remaining dressing.