Gather your ingredients and tools. As you can see I am a big fan of store brands. There are very few "name" brands I will buy over generic or store brands. Most of the time I find the cost savings are far more than any taste or quality difference. Tools I used in making this soup are cutting board, sharp knife for dicing vegetables, kitchen scissors for cutting sausage, dutch oven for cooking, small sauce pan for rue/cheese sauce, wooden cooking spoon, and whisk. I am a firm believer is pre-shredded cheese. The cost is often the same as block and there are less dishes to clean. If you prefer shredding your own cheese, include either a cheese shredder or food processor for shredding.
Cut up the sausage. I have found using my handy dandy kitchen scissors make the process quick and easy.
Heat your dutch oven over medium high heat. Always remember "hot pan, cold oil" helps prevent foods from sticking when browning. When the dutch oven is hot, add the olive oil and butter. When the butter is melted and bubbling (but not brown) add your vegetable and the tsp of pepper.
Cook over medium high heat, stirring frequently to prevent sticking and burning.
Because I am cooking with sausage, a salty food, I wait to add any salt until the potatoes are starting to brown and the onion and carrots are starting to soften. At this point, taste a piece of potato. If it needs salt, add a 1/2 tsp. There should be some nice brown crispies at the bottom of the pan by now. Add the chicken broth and turn the stove to low. Stir, bringing those tasty crispies up from the bottom of the pan. Cover and let simmer for 15 minutes.
While the soup is simmering, start your rue/cheesy goodness, for the soup. Melt 3 tbl of butter over medium heat in a small saucepan. When the butter is melted and bubbling (don't let it brown), add the granulated garlic and onion powder. Give a quick couple stirs with a whisk and add the flour. I usually add a pinch of salt at this point. The mixture will be crumbly. Add the half and half, stirring constantly with the whisk until it starts to thicken. Add the prepared mustard and the cheese, stirring constantly with a spoon, until mostly melted. Remove from heat.
Using the wooden spoon, add the cheese sauce to the soup, stirring constantly until combined. After the sauce is combined with the soup, let it thicken over low heat, stirring occasionally to prevent sticking and burning.
At this point, add the frozen corn. Cook another 5 to 6 minutes until the corn is hot.
Before serving, take a taste and add more salt and pepper if needed. I like to serve with hoagie rolls sprinkled with Italian blend cheese and broiled until melted and crispy.