Preheat the oven to 425°F.
Arrange the mushrooms in a single layer on a baking sheet. Nestle the onion halves into the mushrooms, sprinkle the smashed garlic over, and drizzle with the olive oil. Roast for 20 minutes in the heated oven.
Remove the sheet from the oven and drop the roasted mushrooms and onions into a heavy stockpot. Pour in the broth and wine. Slip the sprigs of thyme into the pot and then bring it all to a simmer over medium-high heat. Continue simmering, covered, for about 30 minutes.
Strain the broth through a fine-mesh sieve, then use a wide-mouthed funnel to pour it into two 1-quart jars, sealing the lids tightly.Cook with the broth right away or store it in the refrigerator for no more than 5 days. Alternately, you can freeze the broth for up to 6 months, making sure to allow plenty of head space if your using glass jars.