In a large pot over medium heat, melt the butter until foamy. Add the diced onion and shredded carrots, stirring frequently for about 5 minutes, until they soften and the onion is translucent.

Stir in the broccoli florets and cook for an additional 3–4 minutes.

Pour in the chicken broth, bringing the mixture to a gentle boil. Once it bubbles, reduce the heat and allow it to simmer for 10 minutes.

In a separate bowl, whisk together the milk, heavy cream, and flour until smooth. Gradually add this mixture to the pot while stirring continuously.

Once the creamy mixture is fully incorporated, season the soup with the kosher salt, black pepper, and crushed red pepper flakes.

Gradually stir in the shredded cheddar cheese until melted and thoroughly combined.

Ladle the hot soup into bowls and serve immediately, pairing it with crusty bread or a crisp salad if desired.