Roughly chop the onion, carrots, celery and garlic and combine with the cauliflower, 2 tablespoons of the olive oil and salt and pepper in a large soup pot. Cook over medium heat until vegetables start to soften and onions become translucent, about 10 to 15 minutes.
Add the bay leaf and chicken broth and bring to a simmer. Cover and cook for 15 to 20 minutes.
Remove the bay leaf and purée the soup until smooth with a hand-held immersion blender, or a conventional blender (see tip below).
Just prior to serving the soup, stir in the gouda, mustard, half-and-half and butter. Taste and season with salt and pepper again if needed. Continue cooking until the cheese has melted and the soup is smooth, 1 to 2 minutes.
In a small pan, heat remaining tablespoon of olive oil over medium-high heat and quickly fry the rosemary and prosciutto until crispy and aromatic.
Divide soup into bowls and garnish with the rosemary and prosciutto.
Notes
Substitutions:
You can easily substitute bacon or pancetta for the prosciutto, as well as cheddar in place of the gouda, if you prefer. If you want a richer, thicker soup, feel free to add more grated gouda.
Cooking Tip:
When using a conventional blender to purée hot soup, allow the soup to cool a little first and work in batches, never filling the blender much beyond the halfway mark.