In a medium sized Dutch oven or pot over medium heat, add olive oil and butter. 

When the butter has melted, add the onions and sauté until translucent, about 4 minutes. 

Add garlic and saute for an additional minute, stirring in with the onions. 

Add salt, red pepper flakes, thyme, stock, potatoes, and broccoli. 

Turn heat to high, bring to a boil, then turn the heat down slightly to simmer for 15- 20 minutes until the potatoes are tender and the broccoli is cooked and easily breaks apart. Add chicken. 

In a bowl or measuring cup, mix together the heavy cream and cornstarch and stir to combine. Add to the soup. 

Allow the soup to come back up to a simmer and simmer for 2-3 minutes. Turn off the heat and stir in the parmesan and the parsley flakes. 

Serve warm.