For the topping:
2 pounds cremini mushrooms, halved if small, quartered if large
1 onion, thinly sliced
2 tsp olive oil
1/4 ounce dried porcini mushrooms, minced after being reconstituted
1 tsp minced fresh rosemary
2 garlic cloves, minced
12 ounces baby spinahc
12 ounces cherry tomatoes, halved
For the polenta:
4 cups water
1 cup coarsely ground cornmeal
1/2 cup Parmesan, divided
1 T unsalted butter, cut into 1/2 inch pieces
For the topping, compile cremini mushrooms, onion, oil, porcini mushrooms, rosemary and 1/4 tsp salt in a large Dutch oven. Cover and cook over medium-low heat, stir occassionally, until the vegetables are softened, 10 to 12 minutes. Uncover, increase the heat to medium-high and continue to cook, stirring occassionally, until the vegetables are lightly browned, 4 to 6 minutes.
Stir in garlic and cook until fragrant, about 30 seconds. Add spinach, one handful at a time, and cook until wilted, 3 to 5 minutes. Stir in tomatoes and cook until just softened. Season with salt and pepper to taste. Cover and set aside off the heat to keep warm.
Meanwhile, bring water and 1/2 tsp salt to a boil in a large, heavy-bottomed saucepan. Slowly add cornmeal, whisking constantly in a circular motion to prevent clumping.
Bring to a simmer, stirring constantly. Reduce heat to low, cover and cook, stirring often and vigorously, making sure to scrape the corners of the pot, until all the polenta becomes soft and smooth, 10 to 15 minutes. Off the heat, vigorously stir in half the cheese and all the butter. Season with salt and pepper to taste.
Divide the polenta among 4 bowls. Divide vegetable mixture evenly among bowls, arranging it on top of the polenta. Sprinkle each portion with remaining cheese and serve.