In a large pot, cook sausage over medium-high heat until cooked through and brown, about 10-15 minutes.
Remove the sausage with a slotted spoon and place in a medium bowl. Make sure to leave all the sausage dripping goodness in the large pot.
Reduce heat to medium/medium-low. Melt the butter in the pan.
Then, add the carrots, celery and onion and cook for 10-15 minutes, until soft and translucent.
Then, add the garlic and stir while it cooks for another 1-2 minutes.
Whisk in the flour, stirring until it gets thick and light brown in color, about 2 minutes.
Add in the ground mustard, cayenne pepper, dijon mustard and beer. Give it a good stir to make sure everything combines.
Bring to a boil and then allow to simmer for 15 minutes.
This next part is optional. Take an immersion blender (or place soup in the food processor) and pulse until the vegetables are ground fine. I did part of my soup like this because I like it chunky, but you could puree the entire soup or you don't have to do this at all! It's preference.
Now, add the cheese, milk and cream to the soup and stir to combine.
Then add the brats back into the soup.
Let simmer for 20 minutes so the flavors can meld, giving it a quick stir every once in awhile.