1️⃣ Sauté Vegetables:
In a Dutch oven or large skillet, melt the butter over medium heat. Add the minced garlic, chopped onion, julienned carrots, sliced celery, salt, and pepper. Cook for about 5 minutes, stirring occasionally, until the vegetables are softened and fragrant.

2️⃣ Make the Roux:
Sprinkle the flour over the softened vegetables, stirring until the veggies are coated and the flour is well combined with the butter. Cook for about 1 minute.

3️⃣ Add Milk and Chicken Stock:
Gradually pour in the milk, stirring constantly to create a smooth mixture. Then, add the chicken stock, stirring well.

4️⃣ Simmer the Soup:
Turn the heat to medium-high. When the soup just begins to bubble, lower it to a simmer (medium-low heat), cover the pot, and cook for 15 minutes, stirring occasionally.

5️⃣ Add Broccoli:
Add the chopped broccoli florets to the pot. Cover and continue to simmer on medium-low for an additional 10 minutes, or until the broccoli is tender.

6️⃣ Add the Cheese:
Remove the pot from heat and gradually stir in the shredded cheddar cheese, a handful at a time, until fully melted and incorporated into the soup.

7️⃣ Serve:
Serve the soup hot in bowls or bread bowls. Enjoy with crusty bread for dipping if desired.