Ready to bring this dream to life? Let’s jump right into the cooking process. Here’s how I whip up this delightful dish.

Start by melting 4 tablespoons of butter in a large pot over medium heat. Once the butter is melted, toss in the diced onion. Let it sauté until translucent, about 2-3 minutes.

The smell wafting through your kitchen will be incredible. Add the minced garlic next, cooking until fragrant (about 30 seconds).

Now it's time for the carrot. This adds sweetness and color! Stir in the thinly sliced or diced carrot and cook for another 2 minutes.

Next, sprinkle in the flour, stirring constantly for about 2 minutes. This forms the base of your soup—trust me, this step is crucial for that creamy consistency.

After the flour has been incorporated, it’s time to pour in the vegetable stock and milk. I like to whisk everything together to avoid any lumps. Bring this mixture to a gentle simmer while continuously stirring.

Once simmering, add the chopped broccoli florets. Cook until the broccoli is tender, about 5-7 minutes. The broth should be thickening nicely, and you’ll notice the vibrant green of the broccoli shining through.

Now comes the most exciting part: the cheese. Gradually stir in the shredded cheddar cheese, mixing until it's melted and combined. This is where the comfort factor really ramps up!

Add the Dijon mustard, fresh thyme, salt, and pepper. Taste and adjust if needed. You might want an extra pinch of salt or a dash more mustard to suit your palate.

Ladle the soup into bowls and finish it with homemade croutons and a sprinkle of nutritional yeast for that added umami kick. Trust me, your taste buds will thank you!