In a large saucepan, bring broth to a simmer over medium-high heat. Remove stems from mushrooms; add thyme sprigs and mushroom stems to broth. Reduce heat to low; gently simmer until ready to use.
In a Dutch oven, heat 4 tablespoons butter and oil over medium heat. Add mushroom caps; sauté until deep golden brown, about 10 minutes. Remove mushroom caps using a slotted spoon, and set aside.
Add onion to Dutch oven; sauté until tender, about 10 minutes. Add rice; cook, stirring constantly, until fragrant, about 1 minute. Stir in wine; cook for 3 minutes, stirring frequently.
Discard mushroom stems and herb sprigs from hot broth. Add 1 cup hot broth to rice mixture; cook, stirring constantly, until liquid is absorbed. Repeat procedure with remaining broth, 1 cup at a time, until liquid is absorbed, 30 to 35 minutes total.
Remove from heat; stir in mushroom caps, cheese, chopped thyme, remaining 2 tablespoons butter, and salt and pepper to taste. Serve immediately.
Recipe by Southern Lady Magazine at https://southernladymagazine.com/wild-mushroom-thyme-risotto-recipe/