In a large pot over medium-low heat saute onions with a pinch of salt in butter, add potatoes in with the onions. Continue cooking until the onions start to soften and become slightly caramelized. About 20 minutes.
Stir in yellow mustard, thyme and a pinch of pepper. Stir in flour to coat the potatoes and the onions.
While constantly stirring add in vegetable base and water. Add in ham and broccoli and allow to warm through, approximately 5 minutes. Stir occasionally (every minute) once flour in completely blended into soup.
Stir in heavy cream, allow to warm for 2 minutes, then stir in cheddar cheese until completely melted into the soup. Serve and enjoy!