In a large pot over medium-high heat, add the butter. Stir until melted, then add the shallots and fresh thyme. Cook until the shallots soften, 4-5 minutes. Dial up the heat a bit, stir in the salt and mushrooms. Cook, stirring occasionally, until the mushrooms release their liquid, and begin to brown, 10 minutes or so.
Add the water (or broth) and bouillon (if you think you need more flavor), and simmer for another 10 minutes or so. Until the broth thickens just a bit. Stir in the wild rice and allow the broth to come back to a simmer. Reduce the heat to low and stir in the grated cheese and cream. Season with more salt if needed and plenty of black pepper.