In a large pot, bring the vegetable broth to a boil. Reduce heat and simmer for 15 minutes.
In a separate skillet, melt the butter over medium heat. Add the onion and cook until softened, about 5 minutes. Add the garlic and cook for another minute until fragrant.
Add the onion and garlic mixture to the simmering broth. Add the bay leaf and white pepper. Continue to simmer for another 10 minutes.
Remove the bay leaf. Stir in the heavy cream and bring to a gentle simmer. Season with salt to taste.
Add the chopped sorrel to the soup and cook until wilted, about 2-3 minutes. Stir in the lemon juice.
Peel the eggs and carefully cut them into quarters, lengthwise.
Place 3-4 pieces of egg in the bottom of each bowl. Ladle the soup over the eggs.