Add the mushrooms, garlic, thyme, pepper, salt, and 1 Tbsp butter to a deep skillet. Sauté over medium heat until the mushrooms have released all of their water and the water has evaporated off the bottom of the skillet.
Add the rice and 2 Tbsp butter to the skillet and continue to sauté for about two minutes more.
Add the vegetable broth to the skillet and stir to dissolve any browned bits off the bottom of the skillet.
Place a lid on the skillet, turn the heat up to medium-high, and allow the broth to come up to a full boil. When it reaches a full boil, turn the heat down to low, or just above low, so the broth remains simmering.
Let the rice simmer for 15 minutes without stirring or removing the lid. After 15 minutes, remove the pan from the heat and let the rice rest for another 5 minutes, without removing the lid.
Finally, remove the lid and fluff the rice with a fork. Taste and add salt or pepper, if desired. Top with chopped fresh parsley as a garnish.