Cut 1 ½ cups of bite-sized broccoli florets and set aside. Coarsely chop the remaining broccoli.

In a large saucepan, heat 1 tablespoon of olive oil over medium heat. Add the onion and cook for about 5 minutes, stirring occasionally, until softened. Add garlic and sauté for 30 seconds.

Sprinkle in the flour and smoked paprika, stirring to coat the vegetables evenly.

Pour in the chicken broth and add the chopped broccoli. Bring the mixture to a boil, then reduce to a gentle simmer. Cook for 8–10 minutes, stirring occasionally, until the broccoli is tender.

While the soup simmers, prepare the croutons. Toss rye bread cubes with the remaining tablespoon of olive oil in a large skillet. Cook over medium heat, stirring occasionally, until browned and crisp, about 10 minutes. Transfer to a bowl.

Puree the soup using an immersion blender or in batches in a traditional blender. (Be cautious with hot liquids when blending.) Return the pureed soup to the saucepan over low heat.

Gradually stir in the smoked Gouda cheese, a handful at a time, ensuring each addition fully melts before the next.

Stir in the reserved broccoli florets and cook for an additional 2–3 minutes until bright green.

Finish with white-wine vinegar, salt, and white pepper. Serve hot, topped with the crispy croutons.