In a large pot, heat up a splash of olive oil over medium heat. Toss in the chopped onion and minced garlic. Sauté these flavor powerhouses for about 5 minutes until they’re softened and fragrant.

Add your diced potatoes along with the broccoli florets to the pot. Stir it around to coat everything in that lovely onion-garlic goodness.

Add your vegetable broth, making sure those veggies are nicely submerged. Bring it all to a boil, then reduce the heat and let it simmer for about 15-20 minutes until the potatoes are fork-tender.

Once the potatoes are tender, use an immersion blender to blend the soup to your desired consistency or carefully transfer the soup to a regular blender in batches.

Return the blended soup to the pot (if needed) and stir in the milk or cream, followed by the shredded cheddar cheese. Keep stirring until the cheese is melted and smooth. Add salt and pepper to taste.

Pour the soup into bowls, sprinkle with croutons or additional cheese if you like, and serve.