Melt one to two tablespoons of butter in a skillet over medium-high heat. Add the diced onion and sauté until it begins to soften—about three minutes. Next, add the diced carrots along with salt and pepper, cooking for another three to four minutes before stirring in the minced garlic for about thirty seconds.

Add the chopped potatoes and chicken stock to your pot. Cover it up and bring everything to a simmer. Allow it to simmer gently for about ten minutes until those potatoes start getting tender.

Once the potatoes are fork-tender, stir in the broccoli florets. Continue simmering until both the broccoli and potatoes are tender—about another ten minutes.

In a small bowl, mix cornstarch into milk until smooth. Stir it into your hot soup slowly.

Finally, add in the shredded cheddar cheese. Stir until it's completely melted and integrated into your soup.

Ladle your delicious soup into bowls and serve hot.