Heat 2 tablespoons of the olive oil in a large deep skillet over medium-high heat until shimmering. Add half the mushrooms in a single layer and cook undisturbed for 3 minutes, then stir and cook 1–2 minutes more until deeply browned. Transfer to a plate. Repeat with the remaining mushrooms, adding oil if the pan looks dry. This hard sear — not crowding the pan — is what gives the dish its flavor.

Reduce the heat to medium. Add the remaining 1 tablespoon olive oil and the onion with 3/4 teaspoon of the salt. Cook, stirring, until softened and golden at the edges, about 4 minutes. Stir in the garlic and thyme; cook 1 minute more until fragrant.

Pour in the white wine (or broth), scraping up every browned bit from the bottom of the skillet. Let it bubble and reduce by about half, about 2 minutes.

Stir in the butter beans, vegetable broth, cream, remaining 1/2 teaspoon salt, and black pepper. Return the mushrooms (and their juices) to the skillet. Bring to a gentle simmer and cook 6–8 minutes, until slightly thickened.

Stir in the spinach a handful at a time until wilted, about 2 minutes. Remove from the heat. Stir in the butter, Parmesan, lemon juice, and lemon zest until the butter melts and the sauce turns glossy. Taste and adjust salt.

Spoon into shallow bowls over or alongside crusty bread. Top with extra Parmesan, thyme leaves, and red pepper flakes if you like.