Heat olive oil in a large pot over medium heat. Add onion and cook for 4 to 5 minutes until softened.
Add garlic and cook for 30 seconds.
Add carrots, potato, smoked paprika, salt, and black pepper. Stir for 1 to 2 minutes.
Pour in the vegetable broth and bring to a gentle boil.
Reduce heat and simmer for 10 to 12 minutes, until the potato and carrots begin to soften.
Add broccoli and simmer for another 6 to 8 minutes, until tender.
Remove from heat and blend part of the soup with an immersion blender, leaving plenty of broccoli and vegetable pieces intact.
Return to low heat and stir in the plant milk.
Add vegan cheddar gradually, stirring until melted.
Stir in nutritional yeast and Dijon mustard.
Taste and adjust salt and pepper.
Serve hot with your favorite toppings or crusty bread.