Add olive oil to a large skillet over medium-high heat. When oil is hot, add bratwurst sausage removed from casings and cook, breaking up with a spatula until no longer pink. Remove with a slotted spoon to your slow cooker.
Add the potatoes, broth, onions, carrots, garlic, thyme, rosemary, mustard, sage, salt and pepper and bay leaf. Mix until well combined.
Cover and cook on high for 4 1/2 hours or low for 7 hours or until potatoes are fork tender.
Remove bay leaf. Use a potato masher to mash some, not all, of the potatoes to thicken the soup. Add the cream and stir until well combined. Cover and continue to cook for 1/2 an hour on low until warmed through. Serve immediately with shredded cheddar cheese for topping, if desired.