Heat the olive oil in a large pot over medium heat. Add the veggies, herbs, and after a few minutes a cup of the broth, lightly cooking.
Add the broccoli florets and liquids, bring to a boil, then reduce heat and simmer for about 3 minutes until the broccoli is tender.
Use an immersion blender to puree the soup until smooth (or blend in batches in a regular blender).
Return the blended soup to the pot, then stir in the coconut cream. Slowly whisk in the cornstarch slurry (recipe below) and let simmer for 3-5 minutes until thickened.
Stir in salt, pepper, herbs, and nutritional yeast, adjusting seasoning to taste. Top with vegan cheddar and croutons.
Cornstarch Slurry
In a small bowl, mix 1 tablespoon of cornstarch with 2 tablespoons of cold filtered water.
Stir well until the cornstarch is fully dissolved, forming a smooth, lump-free liquid.
Slowly pour the slurry into the hot soup while stirring continuously.
Let the soup simmer for 3-5 minutes, stirring occasionally, until it thickens to your desired consistency.
Always use cold water to dissolve cornstarch; adding it directly to hot liquid can cause clumping.