Wash the monk's beard thoroughly under cold water.

Peel the potatoes and halve them if needed so they cook faster.

Wash the radicchio and cut it into quarters or wedges if needed.

Put the peeled potatoes in a pot and cover them with water. Add a teaspoon of salt and the caraway.

Bring the water to a boil and let the potatoes cook for about 15-20 minutes until they are done. Drain the water and set them aside.

Bring lightly salted water to a boil in a small pot. Add the washed monk's beard and blanch it for about 1-2 minutes. It should still be al dente.

Drain the monk's beard and quickly rinse it with cold water to stop the cooking process and preserve its color.

Heat 1 tablespoon of butter in a large pan. Add the blanched monk's beard and sauté it for 1-2 minutes, season with a little salt and pepper. Remove it from the pan.

Add the remaining 1 tablespoon of butter to the same pan. Fry the radicchio for 2-3 minutes until it softens slightly and gets some color. Season it also with salt and pepper.

Heat a non-stick pan over medium heat. Add some oil or butter as desired.

Carefully crack the eggs into the pan and fry them as fried eggs until the whites are set and the yolks are still runny. Season them with salt and pepper.

Distribute the cooked caraway potatoes, the pan-fried monk's beard, and the radicchio onto plates.

Place a fried egg next to each. Serve the dish immediately and enjoy!