In a large pot or Dutch oven, melt the butter over medium heat.
Add the chopped onions and sauté until they are soft and just beginning to turn golden, about 5-7 minutes.
Sprinkle in the flour, lower the heat, and cook for 2-3 minutes, stirring constantly with a wooden spoon to create a roux.
Gradually pour in the hot Potato Peel Broth while whisking continuously to prevent any lumps from forming.
Bring the mixture to a simmer.
Add the washed watercress to the pot and continue to simmer for about 10 minutes, or until the watercress is wilted and tender.
Carefully transfer the soup in batches to a high-speed blender and purée until completely smooth. Return the smooth soup to the pot.
In a separate medium bowl, whisk the heavy cream and eggs together until well combined.
While whisking constantly, slowly pour about 2 cups (480 ml) of the hot soup into the egg mixture to temper it. This prevents the eggs from scrambling.
Remove the soup pot from the heat, and stir the tempered egg mixture back into the main pot.
Season with lemon juice, sugar, salt, and pepper.
Return the pot to a moderate, low heat.
Stir the soup constantly for 3-4 minutes until it has thickened slightly and is heated through. Be very careful not to let it simmer or boil, as this will curdle the eggs.
Serve immediately.
When blending hot liquids, never fill the blender more than halfway.
Remove the small cap from the lid and cover the opening with a folded kitchen towel to allow steam to escape safely.
Don't skip the tempering step for the eggs and cream!
Adding the hot soup slowly prevents the eggs from scrambling, ensuring a silky-smooth, not chunky, texture.
Taste the soup just before serving. The peppery watercress, tangy lemon, and touch of sugar create a complex flavor profile.
Adjust the salt, pepper, or lemon juice as needed to achieve the perfect balance.