Preheat the oven to 375 degrees F and line a half sheet pan with parchment paper.
Spread the cut vegetables onto the pan along with the garlic clove intact (with the skin), top with thyme leaves and drizzle with up to 1/4 cup of olive oil. All the vegetables should be coated.
Season with salt and pepper and roast for 40 minutes. They should be cooked but not charred. Let the vegetables cool and reserve the garlic clove for the dressing. You can also do this ahead of time (up to one day in advance).
In a large serving bowl, add the wild rice, mixed greens, roasted vegetables, basil, feta and capers. Mix to combine.
Squeeze the roasted garlic out of the clove and whisk with the remaining 1/4 cup of olive oil.
Dress the salad with the roasted garlic olive oil and balsamic vinegar and give it another toss to combine.