01 -
Melt the butter in a large heavy-bottomed pot over medium heat. Add chopped onions and cook until they are translucent with lightly golden edges, about 4 to 5 minutes.
02 -
Stir in the all-purpose flour to form a roux. Continue stirring and cooking until the mixture reaches a peanut butter color, approximately 4 minutes.
03 -
Using a whisk, gradually add the chicken broth and half and half, whisking constantly to combine smoothly. Increase heat to medium-high and bring the mixture to a gentle simmer.
04 -
Add broccoli florets and julienned carrots to the pot. Simmer uncovered for 15 minutes, stirring every 3 to 4 minutes to prevent sticking.
05 -
Stir in salt and shredded cheddar cheese until fully melted and incorporated. Adjust seasoning with additional salt if needed. Serve warm.