Step 1

In a large pot over medium heat, melt the butter.

Step 2

Add onions and cook until softened (about 8-10 minutes). Add garlic and cook for an additional minute.

Step 3

Sprinkle the flour over the mixture and stir together until lightly browned (about 5 minutes).

Step 4

Slowly pour in the chicken broth and milk, stirring constantly, until no flour lumps remain.

Step 5

Add the broccoli, carrots, salt, pepper, and nutmeg. Bring the mixture to a simmer, and cook uncovered, stirring occasionally, until the broccoli and carrots are tender (24-26 minutes).

Step 6

Reduce heat to low, and slowly stir in the cheese one cup at a time, fully melting the cheese between each addition.

Step 7

Remove from heat and serve.