Step 1

In a medium, deep skillet with a tight-fitting lid, combine the sunchokes with 1 tablespoon of the butter and stir over moderately high heat until the butter is melted. Add 1/2 cup of water, season with salt and pepper and bring to a boil. Cover and cook over moderate heat until the liquid is evaporated and the sunchokes are tender and lightly browned, 8 to 10 minutes. Transfer the sunchokes to a bowl and wipe out the skillet. Fill the skillet with water and bring to a simmer.

Step 2

In a large saucepan, combine the milk with 1 cup of water, season with salt and bring to a boil. Whisk in the polenta and cook over moderate heat, whisking, until tender, about 5 minutes. Stir in the 1 1/2 cups of shredded cheese and the remaining 2 tablespoons of butter until creamy; stir in a few tablespoons of water if the polenta is too stiff.

Step 3

Crack the eggs into ramekins and gently pour them into the simmering water in the skillet, one at a time. Poach the eggs until the whites are set and the yolks are runny, about 4 minutes. Using a slotted spoon, transfer the eggs to a paper towel–lined plate.

Step 4

Spoon the polenta and sunchokes into shallow bowls and top with the eggs. Garnish with chervil and cheese, sprinkle with truffle salt and serve right away.