Preheat the oven to 400°F and lightly grease a 9x13 baking dish with butter.
Combine the water and milk in a large saucepan and bring to a low boil. Stir in 1 teaspoon of salt. Reduce the heat to low, then gradually pour in the polenta in a steady stream while stirring constantly. Cook, stirring often, until the polenta has thickened, about 3 minutes. Remove the pot from heat, then stir in the butter, green onions, and ½ cup Parmesan cheese. Pour the polenta into the baking dish and spread it out in an even layer.
Meanwhile, heat the olive oil in a large skillet over medium-high heat. Add the onion, mushrooms, and the remaining teaspoon of salt. Cook until the onion is tender and the mushrooms have released their liquid, about 7-8 minutes.
Add the minced garlic and thyme and cook until fragrant, about 30 seconds.
Add the tomatoes to the skillet and cook for 2-3 minutes. Stir in the tomato paste and cook until it has slightly browned. Pour in the wine and deglaze the pan, scraping up any brown bits with a spoon. Simmer until the wine has reduced by about half, about 5 minutes. Add the spinach and cook until it has wilted, about 4-5 minutes. Stir in the basil, then remove the skillet from heat.
Layer the tomato and mushroom mixture on top of the polenta in the baking dish. Crumble in the goat cheese and sprinkle the remaining ½ cup of Parmesan on top.
Transfer the dish to the oven and bake for 25-30 minutes until the cheese has melted. Allow to rest for 5 minutes before cutting into squares and serving.