Sauté the Onion and Garlic: In a large pot or Dutch oven, melt the butter over medium heat. Add the diced onion and sauté for 4-5 minutes until it’s softened. Add the minced garlic and cook for an additional 1-2 minutes until fragrant, stirring often to prevent burning.

Make the Roux: Sprinkle the flour over the onion and garlic mixture, stirring continuously to form a paste. Cook the flour for 1-2 minutes to remove its raw taste, which will help thicken the chowder.

Add the Broth and Potatoes: Gradually pour in the chicken or vegetable broth, stirring well to combine with the roux. Add the diced potatoes, season with a pinch of salt and black pepper, and bring the mixture to a boil. Once boiling, reduce the heat to low, cover, and let the chowder simmer for 15-20 minutes, or until the potatoes are fork-tender.

Add the Broccoli: Add the chopped broccoli florets to the pot, and let the soup simmer for an additional 5-10 minutes, or until the broccoli is tender and bright green.

Incorporate the Milk, Cream, and Cheese: Pour in the milk and heavy cream, keeping the heat on low to avoid curdling. Gradually add the shredded cheddar cheese, stirring continuously until the cheese has melted and the soup is creamy and smooth. Taste and adjust the seasoning with salt and pepper if needed.

Blend (Optional): For a smoother consistency, use an immersion blender to blend part of the soup, or blend half of the soup in a blender and return it to the pot. Leave some chunks for texture if you prefer.

Serve: Ladle the chowder into bowls and garnish with extra shredded cheddar cheese, crumbled bacon, and chopped green onions. Add a dollop of sour cream for an extra creamy touch if desired.