Set pot to saute and add olive oil, ground sausage and diced onions. Brown until sausage is no longer pink and onions have softened. Add garlic and cook 1 more minute together. Turn pot off now.
Pour some of your beer into the pot. Use wood spatula to deglaze and scrape any stuck on meat off bottom of the pot.
Pour in rest of beer. Set to saute again. When it bubbles add mustard and shredded cheese. Stir until it is melted. In a bowl whisk together milk and flour until smooth.
Wait until it bubbles again, then add flour/milk mixture. Stir so it doesn't clump up in soup.
Then add half and half and stir. Allow to bubble. If you like it this texture turn pot off and serve. If you want it thicker add some of your hot liquid from pot into a bowl with cornstarch. Whisk until smooth and add that back in. Allow to bubble and thicken and serve.