• In a heavy-bottomed pot, heat butter over medium until melted. Add shallots, garlic, and carrots, and cook until soft. The shallots should be slightly coloured and translucent.
• Whisk in the flour, paprika, salt, and pepper, stirring to mix completely. Cook for 1 minute.
• Slowly add the chicken broth and the water to the pot while whisking.
• Add the milk and bring up the heat to medium-high. Bring the soup to a very gentle boil, then reduce the heat and simmer for 10 minutes.
• Add the broccoli florets and the corn and simmer partly covered for an additional 20 minutes, stirring occasionally.
• Remove the pot from heat and stir in one small handful of cheese at a time, stirring as you work to ensure that it melts into the soup.
• Use an immersion blender (or transfer to a blender or food processor) to blend the soup to a desired consistency – leave the broccoli as big as you like.
• Add salt and pepper to taste (freshly ground black pepper makes a great addition to this soup).
• Garnish with croutons

Parmigiano Croutons

• Slice the bread into small cubes and set aside.
• Preheat broiler (or use a toaster oven).
• Toast the bread cubes until they're golden brown all over (you'll need to toss them and turn them over a little bit, but it's not the end of the world if they're not brown on every side). Remove them from the oven and sprinkle them with shredded parmigiano cheese, then return toe the oven and heat again until the cheese is a deep golden brown. Remove from the oven and allow to cool.