Preheat oven to 375 degrees. In a large, deep skillet, heat butter until melted.
Add mushrooms to skillet and cook until they've released some of their liquid and begin to brown, about 3-4 minutes. Add onion to the skillet and cook until softened and translucent, another 3-4 minutes.
Add asparagus to the mixture and cook for about a minute. Stir in sliced almonds and rice and cook, stirring until the rice is fragrant and beginning to toast. Sprinkle with salt and add thyme sprigs.
Add boiling water or broth to the pan, scraping up any brown bits on the bottom. Cover with a lid or tightly with foil and bake for about 30-35 minutes until the rice is tender.
Remove from oven and allow to steam for about 5 minutes before uncovering and fluffing with a fork. Stir in Parmesan cheese. Sprinkle with extra almonds before serving if desired.