Melt unsalted butter over medium-low heat in a large pot. Add crushed garlic and sauté for 4-5 minutes until fragrant.

Pour in chicken or vegetable broth and season with salt and pepper. Bring to a gentle boil.

Add diced waxy potatoes, dried marjoram, and whole caraway seeds. Lower heat and simmer for 15-20 minutes until potatoes are tender.

In a small bowl, beat the egg. Gradually add a ladle of hot soup to temper the egg, then stir this mixture back into the pot.

Preheat oven to 350°F (175°C). Cut rye bread into cubes, toss in olive oil, and bake until golden brown.

Ladle the soup into bowls and top with croutons and grated cheese. Serve warm.