Warm a large skillet over medium heat and drizzle in olive oil.
Add the finely diced onion along with the minced garlic and sauté gently until they soften and become fragrant.
Introduce the sliced mushrooms to the pan, cooking until they release their moisture and start to brown.
Sprinkle in the fresh thyme and season with salt and freshly ground black pepper to your liking.
Pour the white wine into the pan, letting it simmer until most of the liquid reduces and the flavors concentrate.
Stir in the orzo pasta, coating it well with the mushroom mixture.
Pour the chicken broth gradually, bring the mixture to a gentle boil, then reduce heat and simmer until the orzo is tender and the liquid is mostly absorbed.
Once the orzo is cooked, stir in the heavy cream and butter, letting them melt and combine into a creamy sauce.
Mix in the freshly grated parmesan cheese and chopped fresh parsley, folding everything together until smooth and well blended.
Adjust seasoning with extra salt and pepper if needed, then remove from heat and serve warm.