Creamy and delicious broccoli cheddar soup made in ONE POT on the stovetop
Add 1 tablespoon butter and olive oil to a large heavy bottomed stock pot/dutch oven over medium heat. Add the diced onion and saute, stirring occasionally, until tender, about 3-5 minutes. Add the minced garlic, paprika, mustard, cayenne pepper, and pepper (I add 1 teaspoon, but add to preference) to the pot. (I like to add the salt AFTER the stock to gauge how much more it needs.) Cook for another 45 seconds to 1 minute stirring constantly until fragrant.
Add in remaining 6 tablespoons butter and melt. Once melted, add in the flour and whisk to combine. Cook for 2-4 minutes, whisking constantly, until the flour is thickened (don't rush or your soup won't properly thicken/taste right).
Gradually add in the chicken stock, whisking constantly. Once all the stock has been added, gradually add in the half and half, again whisking constantly as you add. Reduce heat to medium low, add in the bay leaf, and allow to simmer for 15 minutes or until thickened a bit. (Whisk every few minutes as you chop the broccoli!)
Meanwhile, chop the broccoli and shred the cheese. Add the chopped broccoli florets and matchstick/shredded carrots (give carrots a quick chop in half if they are super long) to the soup.
Allow soup to simmer over low heat for about 15 to 20 minutes, or until broccoli is crisp tender (or tender to your preference!) Stir occasionally. Season to taste with salt (I add about a teaspoon here). (You can blend some of the soup or use an immersion blender here if desired. We like it chunky, but blend to preference if desired)
Add in the cheese and stir until melted. Again taste for seasoning. Serve immediately in bread bowls or regular bowls with a side of bread for dipping!