Peel, quarter, and core the quince. Cut into small pieces.
Peel and dice the celery root, potato, and onion.
Mince the garlic.
Heat the butter in a saucepan over medium heat.
Place a layer of paper towels next to the stove.
Add the speck to the pan. Saute until crispy.
Transfer to paper towels. Pat off excess grease.
Add the onions and garlic to the pan. Fry until the onions become transparent.
Stir in the quince, potato, and celery root.
Cook for 5 minutes, stirring occasionally.
Season with salt and freshly ground black pepper.
Pour the broth into the pan. Bring to a boil. Lower the heat. Simmer for 20 minutes.
When the vegetables become tender (you should be able to easily run a fork through them), use a hand or stick mixer to puree the mixture in the pan. If you do not have a hand mixer, transfer everything to a food processor or blender and puree until smooth, then return the mixture to the saucepan.
Stir in the lemon juice. Season with salt and pepper.
Stir in the chopped parsley.
Mix in the sugar.
Add the white balsamic vinegar 1 tablespoon at a time. Add more or less according to your taste.
Ladle the soup into four soup bowls, garnish with parsley, and serve.