creamy cheddar broccoli soup

My kids love soup.  This soup was a breeze to make and I love that it was full of veggies. 

creamy cheddar broccoli soup (adapted from skinnytaste one & done cookbook)
1 tablespoon butter
1 onion, chopped
1 carrot, chopped
1 celery stalk, chopped
2 garlic cloves, minced
2 tablespoons flour
1/4 teaspoon salt
freshly ground black pepper
2 1/2 cups vegetable broth
1 cup milk
3 big red potatoes, peeled and chopped into small pieces
4 cups chopped broccoli florets, about 2 heads
1 tablespoon freshly grated Parmesan cheese
1 3/4 cups shredded sharp Cheddar cheese

In a Dutch oven or large pot, melt the butter over medium-low heat.  Add the onion, carrot, celery and garlic and cook, stirring until softened 5 to 7 minutes.  Add the flour, salt and pepper to taste and stir until smooth.  Add the chicken broth, milk and potatoes.  Increase the heat to high and bring to a boil.  Reduce the heat to low, cover and cook until the potatoes are soft, 10 to 15 minutes.
Stir in the broccoli florets and Parmesan.  Cook, stirring occasionally until the broccoli is tender, about 8 minutes.  Remove from the heat, add the cheddar and stir well until melted.
Using an immersion blender, blend the soup for a few seconds, leaving some chunks.  Ladle 1 generous cup into each of 6 bowls and serve hot.