Start by washing and cutting the broccoli into small florets. Set aside.
In a large pot or Dutch oven, heat the olive oil over medium heat. Add the diced onion and sauté for about 5 minutes, until it becomes translucent.
Add the minced garlic and cook for another minute, stirring frequently to avoid burning.
Sprinkle the flour over the onions and garlic, stirring to combine. Cook for 1–2 minutes until the flour is lightly golden.
Gradually pour in the vegetable broth while stirring to avoid lumps. Bring the mixture to a boil.
Once boiling, add the broccoli florets, salt, black pepper, and paprika (if using). Reduce the heat to a simmer and cook for about 15 minutes, until the broccoli is tender.
Remove the pot from the heat. If you prefer a smoother texture, use an immersion blender to blend the soup to your desired creaminess.
After blending, return the pot to low heat and stir in the milk. Gradually add the shredded cheddar cheese, stirring continuously until it is fully melted and incorporated.
Taste and adjust the seasoning as needed. Serve hot in bowls and enjoy!