**Sauté aromatics**
- In a large pot or Dutch oven over medium heat, melt the butter or warm the oil.
- Add diced onion and sauté for about 3–4 minutes until softened. Stir in minced garlic and cook for another 30 seconds, being careful not to burn the garlic.
**Add veggies and broth**
- Stir in the chopped broccoli and diced potatoes.
- Pour in the broth, adding enough to fully cover the vegetables. Season with salt and pepper.
- Increase the heat and bring to a gentle boil.
**Simmer until tender**
- Reduce the heat to a simmer. Cover the pot and cook for about 15–20 minutes, or until the broccoli and potatoes are fork-tender.
**Blend (optional)**
- For a chunky soup, leave the vegetables as is.
- For a creamier texture, use an immersion blender directly in the pot or transfer the soup in batches to a blender. Blend until you reach your preferred consistency.
**Add milk or cream**
- Return the soup to the pot (if using a blender). Stir in milk or cream if desired, heating gently without boiling. Adjust seasonings with more salt, pepper, or spices like paprika or nutmeg.
**Serve**
- Ladle the soup into bowls. Top with shredded cheese, croutons, bacon bits, or chopped chives if you like. Serve warm.