Abura-age (aburage, age) is a thinly sliced and deep fried tofu not confused with Atsu-age which is a deep fried whole tofu. When a thinly sliced tofu is deep fried, it puffed up like a tofu pouch. Probably Inari-zushi is the most familiar example to you. The brown sweet skin is the abura-age. Also it is a typical ingredient for a miso soup.
Abura-age is very flavorful since it is deep fried so small amount would add a good flavor to a dish. I often add sliced abura-age to vegetable dishes, and it adds so much flavor. I think it can be a great substitution for meat products, and it is a very versatile useful ingredient that I always make sure to keep a few in my freezer (it lasts longer this way).
My favorite way to eat abura-age is just simply grill it over an open flame and pour some soy sauce while still hot so it absorb the sauce nicely. I would serve it on top of steamy hot rice maybe with a sprinkle of ichimi, Japanese hot pepper. That is one of my favorite lunch when I am alone at home.
Ichimi (Japanese red pepper)
Bowl of rice
Grill abura-age over an open flame or under a broiler. You could also grill on a hot cast iron pan with no oil.
When it is done, sprinkle some soy sauce over it.
Slice abura-age, and put on cooked rice or some other grain of your choice. Sprinkle some ichimi pepper if you would like.