Preheat the oven to 425°F and set the oven rack to the middle position.
Cut about 1/2 inch off the top of the garlic bulb, lightly wrap it in a piece of foil, leaving it partially open at the top. Drizzle about 1 teaspoon of olive oil over the cut top.
Cut the leek into about 1/2-inch round slices. Cut the celery, mushrooms, carrots, and cauliflower into chunks, small enough to fit onto a soupspoon. Place all of the vegetables in a mixing bowl and season with the remainder of the olive oil and salt. Use your hands to toss them well so they're evenly coated.
Lay the garlic packet and the vegetables onto a sheet pan (I like to place a sheet of parchment paper on the pan for easier clean up). Roast them for about 15 minutes, or until they start to turn brown in spots. Turn them over and roast for about 10 more minutes.
Remove the vegetables from the oven and place them in a bowl. Reduce the heat to 350°F, and return the garlic packet on the tray to roast for another 15 minutes, or until it's softened.
When the garlic is soft, carefully squeeze out the individual cloves into the stockpot. It will be hot so you may need to hold it with a cloth or folded paper towels! The garlic cloves should be brown and soft like paste.
Mash the garlic cloves into a paste in the bottom of the stockpot. Add the stock and whisk it to incorporate the mashed garlic. Add the bay leaf, thyme, and wild rice. Bring the soup to a boil, and then reduce the heat to medium-low . Cover and simmer for 30 minutes.
Add the vegetables, and simmer for another 15 minutes, or until the rice is tender. Taste and add extra salt as needed.
Note: You can roast the vegetables and garlic well in advance and prepare the soup when you're ready.