Part 1: Sauté the Mushrooms and Spinach

1. Heat the Pan: Place a large skillet or sauté pan over medium-high heat. Add the 2 tablespoons of olive oil and 2 tablespoons of butter. Allow the butter to melt and foam.

2. Sear the Mushrooms: Add the sliced mushrooms to the hot pan in a single layer. Do not overcrowd the pan; cook in two batches if necessary. Let the mushrooms cook, undisturbed, for 3-5 minutes, until they are deeply browned on one side. This searing process develops a rich, meaty flavor.

3. Continue Cooking: Stir the mushrooms and continue to cook for another 3-4 minutes, until they have released their liquid and it has evaporated, and the mushrooms are golden brown all over.

4. Sauté the Aromatics: Reduce the heat to medium. Add the finely chopped shallot to the pan and cook for 2-3 minutes, until softened and translucent. Add the minced garlic and fresh thyme leaves and cook for another minute until fragrant. Be careful not to burn the garlic.

5. Deglaze the Pan (Optional): If using, pour in the dry white wine to deglaze the pan. Use a wooden spoon to scrape up any browned bits from the bottom of the pan—this is pure flavor! Let the wine simmer and reduce by about half.

6. Add Broth and Spinach: Pour in the ¼ cup of vegetable broth. Then, add the fresh spinach to the skillet in large handfuls. It will look like a lot, but it will wilt down significantly. Gently stir until the spinach is just wilted, about 1-2 minutes.

7. Season and Set Aside: Season the mushroom and spinach mixture generously with salt and pepper to your taste. Remove the pan from the heat, cover it to keep warm, and set it aside while you make the polenta.

Part 2: Cook the Creamy Polenta

1. Boil the Liquids: In a medium to large saucepan or Dutch oven, combine the 4 cups of vegetable broth (or water) and 1 cup of milk. Bring the mixture to a rolling boil over medium-high heat.

2. Whisk in the Cornmeal: Once the liquid is boiling, reduce the heat to low. Very slowly and gradually, pour the cornmeal into the liquid in a thin stream while whisking constantly. This slow addition and constant whisking are crucial to prevent lumps.

3. Simmer and Stir: Continue to cook the polenta on low heat, stirring frequently with your whisk or a wooden spoon, for about 20-25 minutes. The polenta will thicken considerably. Be sure to scrape the bottom and corners of the pot to prevent scorching. The polenta is done when it is thick, creamy, and the individual grains are tender (taste a bit to check).

4. Add the Finishing Touches: Once the polenta is cooked, turn off the heat. Add the 4 tablespoons of butter, the ½ cup of grated Parmesan cheese, the ½ teaspoon of salt, and the ¼ teaspoon of black pepper. Stir vigorously until the butter and cheese are completely melted and incorporated, and the polenta is glossy and luxurious.

5. Serve Immediately: Taste the polenta and adjust the seasoning with more salt and pepper if needed. Ladle the hot, creamy polenta into shallow bowls. Top with a generous spoonful of the warm mushroom and spinach mixture. Garnish with extra Parmesan cheese and fresh thyme leaves. Serve immediately for the best texture.