Place walnuts in a small skillet over medium heat. Cook, shaking and stirring often, until toasted, about 10 minutes. Remove from heat and chop into 1/4 inch size pieces.

Place butter in a large skillet over medium heat. After the butter melts, swirl the pan very often until the butter takes on a golden brown color and smells somewhat like caramel. Add beets, sprinkle with salt and pepper, and turn heat to very low while you cook the agnolotti.

Bring a large kettle of salted water to a simmer. Add agnolotti and stir gently with a slotted spoon until they rise to the surface. Continue simmering 2 minutes. Using a slotted spoon, transfer to the butter and beet sauce and stir to coat.

Divide among warmed bowls, top with toasted walnuts and grated cheese.