In a large saucepan, bring broth to a boil. Slowly pour in cornmeal, stirring constantly. Once polenta has returned to a boil, reduce heat to low and let mixture simmer, stirring often, for 10 to 20 minutes, until polenta thickens slightly and grains become soft.
Stir in milk and continue to cook for another 7 to 9 minutes, until polenta again begins to thicken. Add cheese, butter, and thyme and stir well. The polenta should have the consistency of risotto: Loose but thick. If the mixture is too thick, add some warm water to thin it. It it's too thin, continue to cook until it has thickened. Once polenta is at the desired consistency, remove from heat and cover to keep warm.
In a large sauté pan, heat 2 tablespoons olive oil over medium heat. Add onion and sauté until soft and translucent. Reduce heat to low and add mushrooms, making sure not to crowd them. Cook until mushrooms release liquid and that liquid evaporates. Add another tablespoon of olive oil and garlic to the pan and cook gently for about 5 minutes. Season with salt and pepper to taste.
Spoon polenta into bowls and top with mushrooms. Top with toasted nuts and seeds and serve with a side of greens.