Start by melting 1/3 cup butter in a large skillet over medium heat. As it melts, the aroma of butter will begin to fill your kitchen, setting the stage for the delicious flavors to come.
Once melted, add 1 1/2 cups chopped yellow onion and sauté until the onions start to soften and become translucent, about 3 to 4 minutes. This step is crucial for developing the foundational flavor of your soup.
Next, stir in 2 cloves garlic, minced, along with 6 Tbsp all-purpose flour. Season lightly with salt and freshly ground black pepper. Cook this mixture, stirring constantly, for about 2 minutes. This creates a roux that will thicken your soup.
Slowly whisk in 2 (12 oz) cans evaporated milk, ensuring to whisk well to smooth out any lumps. Continue cooking the mixture, stirring constantly, until it begins to thicken. You’ll notice it getting creamier and richer with each passing moment.
Now it's time to transfer this delicious mixture into your slow cooker. Add 5 cups low-sodium chicken broth, 5 cups small diced broccoli florets, and 1/8 tsp dried thyme. Stir everything together, making sure the broccoli is well incorporated.
Cover with the lid and set your slow cooker to low heat. Let it cook for about 5 to 6 hours. The slow cooking process will allow the flavors to meld beautifully while the broccoli becomes tender.
Once the cooking time is up, turn the heat to warm or off. Stir in 1/2 cup heavy cream, followed by 12 oz sharp cheddar cheese and 2 oz parmesan cheese. Stir well to blend until the cheeses have completely melted, creating a luscious, creamy soup.
Finally, season with additional salt and pepper to taste. Serve warm in bowls, making sure each portion has a good amount of cheesy goodness and broccoli. Enjoy every spoonful!
