Preheat the oven to 350°F/180°C/Gas 4
Melt the 3 tablespoons of butter and toss the baguette pieces with the butter and 3 minced garlic cloves on a rimmed baking sheet. Season with salt and pepper, and place the baguette in the oven to roast for 10-15 minutes until golden and crunchy around the edges. Remove and set aside.
Heat olive oil and the remaining 2 tablespoons of butter in a medium soup pot over medium heat.
Add onion, carrots, and the remaining 2 garlic cloves. Season to taste with salt and pepper. Cook for 2-3 minutes, stirring occasionally, until the veggies soften slightly.
Sprinkle in the flour and dill; stir well. Continue cooking for another minute, just until the raw flour taste cooks out.
Pour in the vegetable stock and bring the soup to a steady simmer.
Once the soup starts simmering, add the broccoli florets and cook for 10-12 minutes until tender.
Add in the milk, heavy cream, and cheddar cheese and continue cooking, stirring constantly, until the cheese melts. Taste and adjust the seasoning, if needed.
Ladle into serving bowls. Garnish with the crispy garlic croutons and additional shredded cheese. Enjoy!