Warm olive oil in a large skillet over medium heat.
Add the diced onion and sauté until translucent and soft, about 5 minutes.
Stir in the minced garlic and cook for an additional 1 to 2 minutes until fragrant.
Toss in the sliced mushrooms and cook until they release moisture and begin to brown, about 8 to 10 minutes.
Pour in the white wine, stirring occasionally, and allow it to reduce by half.
Add the orzo pasta to the pan and stir to coat it well in the mushroom mixture.
Pour in the chicken broth and bring the mixture to a gentle simmer.
Cook uncovered, stirring occasionally, until the orzo is tender and most broth is absorbed, about 15 minutes.
Reduce the heat to low and mix in the heavy cream, butter, fresh thyme, salt, and freshly ground black pepper.
Continue cooking until the sauce thickens slightly, about 3 to 5 minutes.
Remove from heat and stir in the grated parmesan cheese and chopped fresh parsley.
Adjust seasoning if needed and serve warm for a creamy, flavorful dish.