Heat a large soup or stock pot to a medium heat. When the bottom of the pan is hot, add the olive oil. Swirl the pan and add the sausage. Use a wooden spoon to break up the sausage into small pieces. Let the sausage sit so without disturbing it for a few minutes so they bottom can brown. You want to get it crusty and brown so we can lift those little bits up with stock and flavor the broth.
Once the sausage is brown, stir in the carrots, onion and 1 teaspoon salt.. Sauté 3-4 minutes until they start to soften. Stir in the sherry and use the wooden spoon to scrape up any brown bits stuck at the bottom of the pan. Bring to a boil and reduce to a simmer the liquid is reduced by half or more.
When the veggies have softened slightly, stir in the flour. This will help thicken the soup later. Cook for 1 minute.
Reduce the heat to low and add in a cup or so of the broth while whisking the sausage and veggie mixture. Make sure there are no lumps. Slowly whisk in the rest of the chicken broth followed by the half and half. Add in the potatoes and another 1/2 teaspoon salt. Bring the mixture up to a gentle boil over a medium-high heat and then reduce to a simmer. Simmer until the broth has thickened and the potatoes are fork tender, about 15 minutes.
When the soup has thickened and the potatoes are fork tender, turn the heat to low and stir in the cheese. Add in a pinch of nutmeg. Stir until the cheese has melted. Season to taste with salt and pepper. Enjoy with crusty bread!