Caramelize the Mushrooms: Heat 2 tablespoons olive oil and 1 tablespoon butter in a large deep skillet or Dutch oven over medium-high heat. Add the sliced mushrooms in an even layer. Let them cook undisturbed for 3 to 4 minutes until deeply browned on the bottom, then toss and cook for another 3 minutes until tender and caramelized. Season with a pinch of salt and pepper. Transfer half of the browned mushrooms to a small plate for topping later.

Aromatics & Toasting Orzo: Reduce the heat to medium. Add the remaining 1 tablespoon of butter and the minced garlic to the skillet with the remaining mushrooms. Sauté for 60 seconds until fragrant. Add the uncooked orzo and fresh thyme, stirring continuously for 2 minutes to toast the pasta grains lightly in the garlic butter.

Simmer the Orzo: Pour in the warm vegetable or chicken broth and 1/2 teaspoon kosher salt. Stir well, scraping up any delicious browned bits from the bottom of the skillet. Bring the mixture to a gentle boil, then reduce heat to medium-low, cover with a lid, and let simmer for 9 to 11 minutes, stirring every 2 minutes so the pasta does not scorch to the bottom, until tender and most broth is absorbed.

Finish the Cream Sauce: Remove the lid and stir in the heavy cream, freshly grated Parmigiano-Reggiano, fresh baby spinach, and lemon juice. Stir gently over low heat for 1 to 2 minutes until the spinach is fully wilted and the sauce turns luscious, glossy, and velvety.

Garnish & Serve: Top the orzo with the reserved golden caramelized mushrooms, extra grated parmesan curls, freshly cracked black pepper, and thyme leaves. Serve immediately warm right from the skillet.