Step 1: Prep Your Ingredients
Wash and chop the broccoli into bite-sized florets. Don’t discard the stems – peel off the tough outer layer and dice the tender interior. Dice the onion finely and mince the garlic. Shred or finely dice the carrots. Shred the cheddar cheese from a block and set aside. Having everything prepped before you start cooking makes the process smooth and enjoyable.

Step 2: Sauté the Aromatics
In a large heavy-bottomed pot or Dutch oven, melt the butter over medium heat. Once melted and foaming, add the diced onion. Sauté for 4-5 minutes, stirring occasionally, until the onion is soft and translucent. Add the minced garlic and cook for another minute until fragrant. Be careful not to burn the garlic. Add the diced carrots and cook for 2-3 minutes to start softening them.

Step 3: Make the Roux
Sprinkle the flour over the butter-onion-carrot mixture. Stir constantly with a wooden spoon or whisk for 2-3 minutes to cook the flour and create a roux. The mixture will become paste-like and should smell slightly nutty but not burnt. This roux is what will thicken your soup, so don’t skip this step. Make sure to scrape the bottom of the pot to prevent sticking.

Step 4: Add Liquid Gradually
This is crucial for a smooth, lump-free soup! While whisking constantly, slowly pour in about 1 cup of the broth. Whisk vigorously to incorporate the liquid into the roux – it will be thick at first. Once smooth, gradually add the remaining broth while continuing to whisk. Then add the half-and-half and milk, whisking to combine everything into a smooth base. This gradual addition prevents lumps.

Step 5: Add Broccoli and Seasonings
Add all the broccoli florets to the pot. Stir in the salt, pepper, garlic powder, onion powder, nutmeg, and mustard powder (if using). Bring the soup to a gentle boil over medium-high heat, then reduce to medium-low and let simmer uncovered for 15-20 minutes. Stir occasionally to prevent sticking. The broccoli should become tender but not mushy, and the soup will thicken as it simmers.

Step 6: Add the Cheese
This step requires care for smooth, creamy results. Reduce the heat to low. Remove the pot from the burner if you have a hot stove – you don’t want the soup boiling when you add cheese. Add the shredded cheddar cheese in 3-4 additions, stirring after each addition until completely melted and smooth before adding more. Patience here ensures silky smooth cheese integration without graininess or separation.

Step 7: Adjust Consistency and Taste
Once all the cheese is melted and incorporated, assess the consistency. If the soup is too thick, thin it with additional broth or milk until you reach your desired consistency. If it’s too thin (though this is rare), let it simmer a few more minutes to thicken. Taste and adjust seasonings – add more salt, pepper, or a squeeze of lemon juice for brightness if needed.

Step 8: Optional Texture Adjustment
For a smoother, creamier soup, use an immersion blender to partially blend the soup, leaving some chunks for texture. Alternatively, use a potato masher to lightly mash some of the broccoli pieces against the side of the pot. This releases starches that naturally thicken the soup while maintaining a chunky texture.

Step 9: Serve Hot
Ladle the hot soup into bowls. Garnish with extra shredded cheddar cheese, a sprinkle of black pepper, crispy bacon bits, or fresh herbs like parsley or chives. Serve immediately while hot and creamy, alongside crusty bread, crackers, or in bread bowls for an extra-special presentation.