1-First step: Gather and prepare all your ingredients. Start by dicing one whole onion and chopping three cloves of garlic. Cut four heads of broccoli into bite-sized florets. Julienne or finely chop one large carrot. Measure out your butter, flour, milk, half-and-half, and seasonings. Grate 3 cups of cheese doing this yourself rather than using pre-shredded cheese makes a huge difference in texture and melting ability.

2-Second step: In a large pot, melt 1/2 cup of butter over medium heat. Add the diced onion, a dash of salt, and some freshly ground black pepper. Cook for about 5 minutes until the onion has softened and turned translucent. Stir in the chopped garlic and cook for 1 more minute until fragrant. Be careful not to let the garlic burn, as it can turn bitter.

3-Third step: Sprinkle 1/3 cup of flour over the vegetables in the pot, whisking continuously for 1-2 minutes until the flour is golden and has a slightly nutty aroma. This creates a roux, which will thicken your soup. Cooking the flour helps prevent a raw taste and ensures your broccoli cheddar soup will have a smooth texture.

4-Fourth step: Slowly pour in the 4 cups of whole milk and 2 cups of half-and-half, whisking constantly to prevent lumps from forming. Once the mixture is smooth and beginning to thicken, add a pinch of nutmeg, the broccoli florets, julienned carrot, and ½ teaspoon of Dijon mustard. Stir everything together until well combined. The mustard might seem unusual in a broccoli cheese soup, but it enhances the cheese flavor and adds depth to the overall taste.

5-Fifth step: Cover the pot and reduce the heat to low, allowing the soup to simmer for 15-20 minutes until the broccoli and carrot are tender. You can test this by piercing a piece of broccoli with a fork it should slide in easily but still retain some texture. You don’t want mushy vegetables, as they’ll continue to cook slightly after you remove the pot from heat.

6-Sixth step: Reduce the heat to its lowest setting. Gradually add the 3 cups of grated cheese, stirring after each addition until fully melted and creamy. It’s important to add the cheese slowly over low heat to achieve the smoothest possible texture. If you add it all at once or over high heat, the cheese oils can separate from the milk solids, resulting in a grainy broccoli cheddar soup.

7-Final step: Season your soup with additional salt and pepper to taste. At this point, you have three options for the texture of your broccoli cheese soup:
– Serve it chunky, with whole broccoli florets
– Mash it slightly with a potato masher for something between chunky and smooth
– Puree it completely in a blender for a velvety texture

If you choose to puree the soup, return it to the heat afterward and thin with 1-2 cups of chicken or vegetable broth if needed to reach your desired consistency.