Heat the oil over medium-high heat in a large pot (5-6qt). Add the celery, carrot, red pepper, and garlic, and cook for about 5 minutes or until the veggies soften slightly.
Add in the flour, stirring constantly and cook for another minute.
Whisk in the non-dairy milk, vegetable broth, mustard, and paprika. Bring the mixture to a boil until it thickens slightly.
Add the broccoli florets and let them cook until they become tender, which should take 5 to 8 minutes.
Reduce the heat to medium-low, then stir in the vegan cheddar shreds. The cheese will contribute to the soup's thickness. Season the soup with salt and pepper to suit your taste.
To finish, garnish the soup with more vegan cheddar shreds and a few twists of freshly cracked black pepper.