How to Make It
Preheat a gas grill to medium-high (400°F to 450°F). Cut squash lengthwise into 30 (¼-inch-thick) slices total using a mandoline or a sharp knife. (Discard remaining squash, or reserve for another use.) Brush squash slices evenly with oil on both sides, and sprinkle both sides with pepper and 1 teaspoon of the salt.
Place slices on oiled grates; grill, uncovered, until slices are tender and grill marks appear, about 3 minutes per side. Remove from grill.
Stir together goat cheese, lemon zest, tarragon, and remaining ¼ teaspoon salt in a small bowl.
Spoon ½ teaspoon cheese mixture onto 1 grilled squash slice about ½ inch from 1 end. Top cheese with 1 basil leaf, and roll up the squash slice. Place roll-up, seam side down, on a serving platter. Repeat process with remaining cheese mixture, squash slices, and basil leaves. Serve chilled or at room temperature.