Melt butter in a stockpot over medium heat. Add chopped onion, carrot, and celery. Saute until softened. Add flour. Cook for about 5 minutes, stirring often.
Add chicken broth and beer. Heat until it comes to a boil.
Slowly add cheese while stirring until just boiling and smooth. Add half-and-half, salt, dry mustard, jalapenos, and Worcestershire sauce. Reduce heat to low and cook until soup has thickened.
Cut smoked sausage into 1/2-inch pieces and place in a saucepan. Saute sausage over medium heat until heated through. It will probably take about 5 to 7 minutes. Add sausage to the soup, transfer to a large serving bowl and serve hot.