Soy sauce in solid form is an excellent description. I actually do this in reverse in Taiwan, where they have a type of thick soy sauce called 醬油膏. It's used in the local cuisine to build umami flavor in sauces and stir-fries or sometimes as a condiment, but it also works as a marmite-replacement. I tend to put it in a dish with some olive oil for margarine-replacement and dip chunks of bread into it to get my "foreign" food fix.

I imagine most people from soy sauce eating countries in Asia would understand the flavor profile, it might be more the combination with toast that feels unexpected.