1. Melt the butter in a large pot or Dutch oven over medium heat. Add the onion, salt, and several grinds of pepper and cook, stirring, for 5 minutes, or until softened. Stir in the garlic and cook for another minute, then sprinkle in the flour and whisk continuously for 1 to 2 minutes, or until the flour turns golden. Slowly pour in the milk, whisking continuously.

   
   

2. Add the broth, broccoli, carrot, and mustard and stir to combine. Simmer for 15 to 20 minutes, or until the broccoli is tender.

   
   

3. Gradually add the cheese*, stirring after each addition, until all the cheese is melted and the soup is creamy. Season to taste and serve with homemade bread, if desired.

Notes:

• Grate the cheese yourself. Pre-shredded cheese is often coated in anti-caking agents that can prevent the cheese from melting into a lusciously creamy soup. To ensure that your broccoli cheddar soup has the best smooth and creamy texture, buy a block of cheese and grate it yourself.

• Whisk continuously when you add the flour and milk. At first, whisking prevents the flour from burning on the bottom of the pot with the butter. Once you add the milk, it evenly disperses the flour and butter in the liquid, thickening the soup and preventing lumps from forming.

• Go low and slow. When you add the cheese to the soup, make sure that the pot is over very low heat. If the heat is too high, the cheese won’t incorporate into the soup, giving it a thin, gloopy texture. I also recommend adding a little at a time and stirring well between additions.

• Reheat it on the stove. Leftovers will keep in an airtight container in the fridge for up to 3 days. To reheat them, you’ll once again need to go low and slow. Skip the microwave, and warm the soup on the stovetop instead. Place it in a saucepan over medium-low heat, and stir occasionally until heated through. Reheated this way, the soup should stay thick and creamy. If you try to rush the process and crank up the heat, the soup will separate. Trust me, I learned the hard way!