In a large pot, melt 1–2 tablespoons of butter over medium-high heat. Add diced onion and sauté until translucent, about 3 minutes.

Stir in diced carrots, a pinch of salt, and ground pepper. Cook for another 3-4 minutes until softened.

Add minced garlic and sauté for 30 seconds until fragrant, combining well to infuse flavors.

Introduce potatoes and chicken stock. Cover and simmer for about 10 minutes until potatoes begin to soften.

Incorporate broccoli florets and cook for another 10 minutes until bright green and tender.

Mix cornstarch with a splash of milk until smooth, then stir into the soup and cook until thickened.

Remove from heat, stir in shredded cheddar cheese until melted. Adjust seasoning if necessary.

Ladle warm soup into bowls and serve immediately, pairing with crusty bread or salad.