Peel the potatoes and trim the leaves off the cauliflower. Cut everything into 1′-2″ chunks
Melt the butter with the olive oil in a large pot. Saute the onions in the pot for 2-3 minutes until they begin to soften and sweat. Add the garlic and cook 1 more minute, but don’t let anything brown.
Pour in the vegetable broth and milk. Add the cauliflower and potatoes and turn up the heat to bring it to a vigorous boil. Turn the heat down to maintain a low simmer for 20 minutes and the vegetables a re soft.
Use an immersion blender on high speed to puree the bisque until smooth and silky. Add the salt, pepper and heavy cream. Blend again briefly to integrate the seasoning. Taste and adjust seasoning if necessary.
Keep warm while preparing the fried shallots or allow it to cool, cover and refrigerate until ready to serve
Ladle the soup into bowls and garnish with a haystack of fried shallots