Toss onion and carrots into the food processor and pulse a few times.

Heat butter in a large stockpot over medium-high heat until melted. Add onions and carrots and sauté for 5 minutes, stirring occasionally until onion is translucent. Stir in garlic and sauté for an additional 1-2 minutes. Stir in the flour and sauté for an additional minute.

Stir in the chicken stock until it’s combined, then add milk. Continue cooking until it reaches a simmer. Reduce heat to medium. Add in the broccoli and simmer until broccoli reaches desired level of tenderness, then add the salt, pepper and cheese. Simmer long enough to melt cheese, taste, and add additional salt and pepper as desired.

Serve promptly with a side of crusty French bread for a perfect pairing. Enjoy!