Cut your cauliflower into uniform, bite-sized pieces so they cook evenly. Slice the mushrooms about ¼-inch thick.

Heat 2 tablespoons of olive oil in a large skillet over medium-high heat until it shimmers but doesn't smoke.

Add cauliflower florets to the hot skillet in a single layer. Let them cook undisturbed for 3-4 minutes until they develop golden-brown spots on the bottom. Stir and cook another 2-3 minutes until fork-tender.

Push cauliflower to one side of the skillet. Add remaining olive oil and butter to the empty space. Once butter melts and begins to foam, add sliced mushrooms and diced onion. Cook for 4-5 minutes, stirring occasionally, until mushrooms are golden and onions are translucent.

Add minced garlic, thyme, and paprika to the skillet. Stir everything together and cook for another minute until fragrant. Season generously with salt and pepper, then sprinkle with fresh parsley and Parmesan if using.