Heat oven to 350° F.
Bring 4 1/2 cups water to a boil. Whisking constantly, slowly add the polenta. Add 1 1/2 teaspoons of the salt and the butter. Reduce heat and simmer, stirring frequently, for 10 to 15 minutes. Stir in the cream cheese and 1/2 cup of the Gorgonzola.
Meanwhile, in a large skillet, over medium-high heat, warm 2 tablespoons of the oil. Add half the mushrooms and cook for 6 minutes. Add half the shallot and cook for 2 minutes more. Transfer to a plate. Repeat with the remaining oil, mushrooms, and shallot. Season the mushrooms with the pepper, thyme, and the remaining salt.
Butter an 8- or 9-inch baking dish or eight 6-ounce ramekins. Stir 2/3 of the mushrooms into the polenta and transfer to the prepared dish or ramekins. Top with the remaining mushrooms and Gorgonzola. Bake, uncovered, until the Gorgonzola has melted, about 15 minutes.