Heat 2 tablespoons of olive oil in a large Dutch oven or pot over medium heat. Add the chopped onion and cook until softened, about 5-7 minutes. Add the sliced garlic and cook for 1 minute more until fragrant.

Stir in the chopped broccoli and vegetable broth. Bring to a boil, then reduce heat to a simmer, cover, and cook for 15-20 minutes, or until the broccoli is very tender. Season generously with kosher salt and freshly ground black pepper.

Carefully transfer half of the soup to a blender and blend until smooth. Return the blended soup to the pot with the remaining chunky soup. Alternatively, use an immersion blender to blend half the soup directly in the pot, leaving some chunks for texture.

Reduce heat to low. Gradually stir in the shredded sharp cheddar cheese, a handful at a time, until completely melted and smooth. If desired, stir in the heavy cream for extra richness.

While the soup is simmering, preheat oven to 375°F (190°C). Toss the cubed baguette with 1 tablespoon of olive oil on a baking sheet. Spread in a single layer and bake for 8-10 minutes, or until golden brown and crispy. Season with a pinch of salt if desired.

Taste the soup and adjust seasonings as needed. Serve hot, garnished with the toasted croutons and an extra sprinkle of black pepper.