In a large pot, heat the extra-virgin olive oil over medium heat. Once the oil is shimmering, add the finely diced onion. Sauté the onion for about 3-4 minutes, or until it becomes tender and translucent.
Stir in the minced garlic and cook for an additional 1 minute, or until fragrant and aromatic. Be careful not to let the garlic burn.
Pour in the vegetable broth and bring the mixture to a gentle boil. Once boiling, add the fresh broccoli florets. Cook for 10-12 minutes, or until the broccoli is vibrant and tender but not mushy.
Carefully remove the pot from heat. Using an immersion blender, puree the soup to your preferred consistency, whether smooth and creamy or with a bit of texture. If you don’t have an immersion blender, transfer the soup in manageable batches to a countertop blender, blending carefully to avoid splatters.
Once pureed, return the soup to the pot if using a blender. Stir in the heavy cream (or coconut cream) until well incorporated and smooth.
Gradually sprinkle in the freshly shredded cheddar cheese, stirring continuously until it fully melts and is incorporated, creating a velvety texture.
Mix in the mustard powder and ground black pepper, adjusting salt to taste. Allow the soup to simmer gently for an additional 5 minutes, stirring occasionally to ensure nothing sticks to the bottom of the pot.
Remove the pot from heat and allow the soup to cool for a few minutes before ladling into bowls.
Notes
For an inviting finish, top with croutons and extra shredded cheese.