Melt the butter in a large pot or dutch oven over medium-low heat.
Add the diced onion, carrots, garlic, and a pinch of salt and pepper to the pan and stir.
Cover the pot and allow the vegetables to cook for 6 minutes, stirring occasionally.
Turn the heat up to medium. Sprinkle the flour over the vegetables and cook, whisking constantly for 2 minutes.
Slowly whisk in the chicken stock until smooth
Add the broccoli florets to the pot. Simmer for 5-6 minutes, until broccoli is tender.
Meanwhile, in a medium bowl whisk together the heavy cream, sour cream, dijon mustard, and hot sauce.
Add 1 ladle full (about ½ cuof the broth from the soup to the cream mixture and whisk to combine.
Pour the heavy cream mix into the soup while whisking constantly. Taste the soup at this point, add salt & pepper to taste.
Remove the pot from the heat and stir in the shredded cheese in 3-4 handfuls until fully melted and smooth.
OPTIONAL FOR A SMOOTHER SOUP: Remove 1 ladle full (about 1 cup) of the soup from the pot into a bowl. Use a hand held immersion blender to carefully puree the soup to desired consistency. Return the reserved soup the the pot. OR, puree the soup in 2-3 batches in your blender until smooth.