In instant pot on saute setting, melt butter. After it is melted, immediately add the onion, carrots and garlic. Saute approximately 1 minute or until onion is soft.
Reduce heat to low and add flour. Stir briskly and saute for 30 seconds.
Add chicken stock in 2-3 batches stirring well so there are no lumps. Using a whisk helps with this.
Add the seasonings and mustard and deglaze the pot sides and bottom .
Turn off the pot and add the broccoli florets and mix well.
Close and seal instant pot. Cook on high pressure for 1 minute.
Add room temperature or warm (heat in microwave) half and half. Do not add cold.
Mix everything well and saute on low. Bring soup to a simmer.
Immediately turn off instant pot once soup begins to simmer.
Add cheese in 2-3 batches and stir well until cheese fully melts and combines into the soup.
Serve with toppings of your choice, such as shredded cheddar, chopped broccoli, hot sauce, sour cream, chives….