Sauté the Aromatics

1. In a large pot, melt the butter over medium heat.
2. Add the diced onion and cook for 4-5 minutes until it becomes translucent.
3. Stir in the minced garlic and dried thyme, cooking for an additional 1-2 minutes until fragrant.

Create the Roux

1. Sprinkle the flour over the onion mixture, stirring constantly for 2-3 minutes to cook off the raw flour taste.
2. This forms a thick paste (roux) that will help thicken the soup.

Add the Broth and Potatoes

1. Slowly pour in the chicken stock, stirring continuously to incorporate the roux into the liquid. Add the diced potatoes and season with salt and black pepper.
2. Bring the mixture to a boil, then reduce the heat and let it simmer for 10-12 minutes, or until the potatoes are fork-tender.

Cook the Broccoli

1. Add the chopped broccoli florets to the pot, stirring to combine.
2. Continue to simmer for 5-7 minutes, until the broccoli is tender but still vibrant in color.

Add the Cream and Cheese

1. Stir in the heavy cream, then gradually add the shredded cheddar cheese, stirring until melted and smooth.
2. Avoid boiling the soup at this stage to keep the cheese from curdling.
3. Taste and adjust seasoning with additional salt and pepper if needed.

Serve and Enjoy

1. Ladle the warm soup into bowls and serve immediately with crusty bread or crackers.
2. Garnish with extra shredded cheddar or a sprinkle of thyme if desired.