1. Bring 1 quart (1 liter) water to a boil in a medium saucepan over high heat. In a bowl, whisk the polenta and 1 cup water until smooth. Whisk the polenta mixture into the boiling water. Reduce the heat to medium. Cook, stirring constantly, about 5 minutes, or until thickened. Reduce the heat to low, cover, and cook 20 minutes, until soft. Season lightly with salt.

2. Meanwhile, place a heatproof bowl over a saucepan of gently simmering water. Add the butter and let it melt. Add the cheese and milk and cook, stirring often, until the cheese melts. Beat in the egg yolks and cook until the cheese sauce is lightly thickened. Season with pepper.

3. Divide the polenta among 4 bowls, and make an indentation with a spoon in the center of each. Top each with the cheese sauce, then the raw sliced mushrooms. Serve hot.