Bring water, butter and salt to a boil in a large saucepan. Whisk in the polenta in a thin stream and constantly stir for 3-4 minutes to remove any lumps. Reduce to a simmer, stirring occasionally (about every 5 minutes), for 45 minutes until polenta is smooth and creamy. Add more water during the process if polenta gets too thick. Also, note that polenta tends to “burp” and shoot out at you while cooking—so be careful!
While polenta is cooking, heat oil in a saucepan over medium heat. Add garlic, onion, leeks, red pepper flakes, thyme and salt, and cook, stirring occasionally for about 5 minutes until onion start to soften. Add carrots and cook for an additional 2 minutes.
Add mushrooms and continue cooking, stirring occasionally until most of the liquid from the mushrooms is soaked up. Stir on tomato paste, wine, water, and beans and cook for an additional 5 minutes, until the sauce has slightly reduced and the beans are heated through.
Season with salt and pepper.
Once the polenta has cooked for 45 minutes, stir in the milk, parmesan cheese, salt and pepper. Keep warm until ready to serve. When cooked polenta is cooled it gets lumpy and hard, so be sure to keep it warm before serving.
Serve warm mushroom and butter bean ragout with creamy parmesan polenta.