Heat a gas grill to high. Brush both sides of the zucchini with olive oil and grill with the grill cover down, until browned and limp, 3 to 4 minutes per side. Transfer the grilled zucchini to a cooling rack to keep them from steaming as they cool. In a bowl, combine the goat cheese, salt, sun-dried tomatoes, oil, and thyme. Spread 1 heaping teaspoon of the filling thinly over one side of each grilled zucchini strip (use a mini spatula or your fingers to spread). Roll up the zucchini (not too tightly; this is more like folding), and put them on a baking sheet lined with parchment or foil. Refrigerate if not using within an hour, but bring back to room temperature before broiling. Heat the broiler. Sprinkle with a little grated Parmigiano and brown under the broiler, about 1 minute. *To slice zucchini for roll-ups, trim off both ends. Then even the rounded long sides by trimming just a little bit off. Cut the remainder lengthwise.