Heat a drizzle of olive oil in a large pot over medium-high heat and arrange half the sliced mushrooms across the bottom. Let the undersides develop a golden-brown surface before turning them rather than stirring continuously.

Turn the mushrooms, season with salt and pepper, finish browning them, and transfer them to a bowl; cook the remaining mushrooms the same way, adding oil as needed. Both batches should have browned edges and a deeper, nutty aroma instead of looking pale and wet.

Use the same pot to melt 1 tbsp butter, soften and lightly brown the diced onion, then stir in the garlic for about 30 seconds. The onion should look tender, and the garlic should smell fragrant without taking on dark color.

Add the white wine and simmer for about 5 minutes, using the spoon to loosen the browned residue from the bottom. Wait until almost all the wine has evaporated and only a little concentrated moisture remains.

Add the uncooked orzo and browned mushrooms, followed by the stock, cream, parsley, and thyme, then stir and bring everything to a simmer. The pasta should sit in a loose, creamy liquid with the mushrooms and herbs distributed throughout.

Reduce the heat slightly and cook at a gentle simmer, stirring frequently across the bottom until the orzo reaches al dente. The liquid should thicken into a glossy sauce while the pasta becomes tender with a small amount of resistance at its center.

Move the pot off the heat, incorporate the Parmesan and remaining 1 tbsp butter, adjust the salt and pepper, and loosen with hot stock or water if needed. The finished orzo should flow softly when stirred rather than hold together as a stiff mound.