Preheat the oven to 400°F. Gently remove any visible dirt from the mushrooms with a damp paper towel rather than rinsing them with water. Trim away any dark or dried portions from the stem ends. Keep the mushrooms whole, cutting only especially large ones in half so they roast at a similar rate.
Arrange the prepared mushrooms across a baking sheet in a single, even layer.
In a small bowl, whisk together the vegetable oil, balsamic vinegar, and soy sauce until thoroughly blended.
Add the finely minced garlic and chopped fresh thyme to the liquid mixture. Season with salt to taste and several grinds of fresh black pepper, then stir until the seasonings are evenly incorporated.
Pour the balsamic-soy mixture over the mushrooms. Gently toss until each mushroom is thoroughly coated, then redistribute them into a single layer so they can brown and caramelize rather than steam.
Transfer the baking sheet to the preheated oven and roast the mushrooms for 10 minutes.
Carefully remove the pan from the oven. Stir the mushrooms thoroughly, scraping up any caramelized portions from the bottom of the baking sheet and redistributing the glaze over the mushrooms.
Return the mushrooms to the oven and roast for an additional 10 minutes, or until they are tender and golden brown and the cooking liquid has reduced to a shiny glaze.
Transfer the roasted mushrooms to a serving dish while they are still warm. Serve immediately as an appetizer or side dish.