Stir 1/4 cup water, 2 tablespoons butter, and salt together in a pot; bring to a simmer. Reduce heat to medium and whisk flour into butter mixture until a paste-like dough forms, 2 to 3 minutes. Transfer dough to a bowl to cool, 5 to 10 minutes. Whisk egg into cooled dough until completely incorporated. Refrigerate until chilled, at least 30 minutes.

Melt 2 tablespoons butter in a pot over medium-low heat. Cook and stir onion, garlic, and a pinch of salt in hot butter until onion is soft and translucent, 5 to 10 minutes. Add cauliflower, 2 cups water, and chicken stock. Bring to a simmer and cook until cauliflower is tender, about 30 minutes.

Puree soup using an immersion/stick blender until smooth. Stir cream, nutmeg, cayenne, and a pinch of salt into soup. Reduce heat to low to keep soup warm while making the fritters.

Heat oil in a deep-fryer or large saucepan to 350 degrees F (175 degrees C).

Fold crumbled blue cheese into chilled fritter batter until cheese is coated with dough. Spoon dough into a teaspoon and transfer to a second teaspoon to form a fritter. Drop fritters into oil and cook in the preheated oil until the outside is golden brown and cheese is melted on the inside, 2 to 3 minutes. Ladle soup into bowls and top with fritters and chives.