Heat olive oil in a large pot over medium heat.
Add onion and garlic, sauté until golden and fragrant.
Toss in carrots and broccoli, then pour in vegetable broth.
Bring to a boil, reduce heat, and simmer for 10–12 minutes until veggies are tender.
Scoop out half the mixture and blend until creamy (or use an immersion blender).
Return it to the pot and stir in coconut milk, nutritional yeast, and vegan cheddar.
Add cornstarch slurry, salt, pepper, and paprika; stir until thick and luscious.
Simmer for 5 more minutes, letting the flavors mingle like best friends with secrets.
Taste, adjust seasoning, and serve hot with croutons, cheddar shreds, and parsley.
Enjoy with your favorite blanket and zero responsibilities.