In a large pot, heat olive oil and butter over medium heat. Once the butter melts, add diced onion and cook for about 3–4 minutes until softened and fragrant.

Lower the heat to medium-low, then sprinkle in the flour. Stir continuously for about 2–3 minutes to form a smooth roux — this will thicken your soup later.

Gradually pour in the chicken broth while stirring to remove any lumps. Add the bouillon powder, onion powder, garlic powder, salt, and black pepper. Mix well, then toss in the chopped broccoli and shredded carrots.

Bring the soup to a gentle boil, then reduce the heat and let it simmer for 10–15 minutes, stirring occasionally, until the veggies are soft.

Remove from heat and let it cool slightly for a couple of minutes. Stir in the heavy cream, then slowly add the shredded cheddar cheese in small handfuls, mixing until melted and smooth.

Ladle the soup into bowls and enjoy it warm — optionally with crusty bread or a sprinkle of extra cheddar on top.