Combine the first 6 ingredients, 1/4 tsp cumin, and 1/4 tsp cayenne pepper in a medium saucepan. Cook it until the onions are soft and translucent, about 4-5 minutes.
While your vegetable mixture is cooking, whisk the cornstarch into the coconut milk and set it aside.
When the vegetable mixture is done cooking, pour it into a bowl and set it aside.
Add the butter, coconut milk, 1/8 tsp cumin, and 1/8 tsp cayenne pepper to your pan and bring it to a simmer.
Cook the milk mixture for 3-4 minutes, stirring constantly, until it is slightly thickened. It will not be very thick at this point, but it should have thickened up some.
Add the shredded cheese to the milk mixture very slowly (about 2-3 tablespoons at a time), while whisking constantly.
Once all of the cheese is thoroughly mixed in, stir the vegetable mixture back in. Keep it on the stove until the it is heated through, then serve.