Cut sausage into ½-inch slices.
Heat oil in a skillet over medium heat. Add potatoes and sausage to skillet and stir until cooked through.
Add broccoli to skillet and simmer on low heat.
In a separate saucepan, stir whipping cream over medium heat for two minutes. Reduce heat to low and whisk in shredded cheese until cheese is fully melted.
Add salt and pepper to taste.