COOK ONIONS
1-Melt butter to a large heavy-bottomed pot: Melt butter to a large heavy-bottomed pot over medium heat.
2-Add onions and cook until lightly golden: Add onions and cook until lightly golden brown on the edges and the onions are translucent about 4-5 minutes.

MAKE ROUX
3-Make a roux by stirring in the: Make a roux by stirring in the flour. Continue to stir and cook the flour mixture until the roux turns the color of peanut butter. This will take about 4 minutes.

MAKE SOUP
4-Grab a whisk and slowly pour in: Grab a whisk and slowly pour in the chicken broth and half and half while whisking constantly.
5-Turn the heat up to medium-high and: Turn the heat up to medium-high and bring the soup to a slow bubble. Once bubbling, reduce the heat to simmer.

SIMMER SOUP
6-Stir in the broccoli florets and carrots: Stir in the broccoli florets and carrots. Simmer the soup for 15 minutes, stirring every 3-4 minutes.

TO FINISH
7-Stir in the salt and cheddar cheese: Stir in the salt and cheddar cheese until the cheese is nice and melted.
8-Season the soup to taste with additional: Season the soup to taste with additional salt. Serve.