Cut out the pepper stems and then slice each lengthwise along the ribs or ridges into 3 or 4 large triangular wedges. Trim the stem and blossom ends from the zucchini and squash and cut them lengthwise into thin slices. Trim the eggplant and cut crosswise into 12 slices 1/4 to 3/8-inch thick. Peel the onion and cut into 1/4-inch slices.
Trim the portobello mushroom stem even with the cap so it will lie flat on the grill. Brush all over with 1/2 tablespoon of the Rosemary Garlic Oil. Set aside.
Set a cast iron grill pan over high heat and coat with vegetable cooking spray. Let it warm up for 3 to 5 minutes (or light your outdoor grill). Using a pastry brush, coat the zucchini, squash, eggplant, and red onion slices with about 2 1/2 tablespoons of the remaining oil; it will be a very thin film, but it should be enough. The peppers do not need any. Grill the vegetables, except the onion in batches as necessary, on each side, rotating them 45 degrees to make cross-hatch grill marks. They should be cooked until they are nicely browned, but not charred, cooked through but still hold their texture. The peppers will have black marks on the outside, but they are eaten with their skin and bright color intact. Grill the mushroom stem side down first, so when it is turned and finishes cooking, the juices will be retained. Reduce the heat to medium high and grill the onion, turning and rotating as described, until tender and browned but not burned. Here are the approximate cooking times, which will vary with your grill: Peppers - 6 to 7 minutes per side Zucchini and squash - 2 to 3 minutes on first side, 2 minutes on second Eggplant - 4 to 6 minutes per side Red Onion - 3 to 4 minutes per side Portobello - 5 to 6 minutes per side As the vegetables are cooked, transfer them to plates or a large baking sheet lined with wax paper. Transfer the portobello to a cutting board and let cool for at least 5 minutes; then slice. Be sure to reserve any mushroom juices. Season the grilled vegetables and mushroom lightly with salt and pepper.
Line a large round or oval serving platter with the arugula. Arrange the grilled vegetables decoratively in bunches around the edge of the platter. Pile up the pepper wedges in the center.
In a small bowl, whisk together the balsamic vinegar and lemon juice with the remaining Garlic Rosemary Oil. Mix in any reserved mushroom juices. Drizzle evenly over the salad. Crumble goat cheese on top. Serve at room temperature.
Combine all the ingredients in a small glass jar with a lid. Let stand at room temperature at least 15 minutes, preferably 1 hour. If not using within several hours, cover and refrigerate for up to a week.;