Eggplant, Avocado and Nagaimo Gratin ナスとアボカドの長芋グラタン

I made this dish for lunch one day from what we had on hand and what we need to finish before it went bad. I just winged it without any particular recipe. As a result I was not sure how it would come out but it was certainly edible and quite interesting (in a good way).

The main items are Asian eggplant, avocado and grated nagaimo mixed with an egg (in leu of Béchamel sauce). I also added tomato and shiitake mushroom sautéed with shallot, just because I had them.

Ingredients:
One Asian eggplant (pale purple and long), cut into a bite size by cutting at 45 degree angle as I turned the egg plant (“Rangiri” 乱切り)
One avocado, cut into a bite size pieces similar to the eggplant (I only had half of a leftover avocado).
Nagaimo, about 200grams, peeled and grated
One large egg
3 skinned Campari tomatoes, seeds removed and cut into small cubes
1 tbs of chopped shiitake mushroom and shallot sautéed in olive oil (I made this few says ago mostly from the stems of the shiitake mushrooms)
Cheeses (I used sharp cheddar and parmesan but any melting cheese will do), the amount is arbitrary
2-3 tbs olive oil

Directions:
Sauté the eggplant in 2 tbs of olive oil the skin side down first then brown all other sides (4-5 minutes)
Place the eggplant and the avocado in the bottom of a small Pyrex baking dish.  Add the remaining 1tbs olive oil.
Mix the grated nagaimo and the egg and pour over (see below)

Top with the mushroom mixture, the tomatoes, and the  cheeses and bake for 30 minutes at 350F (I used the toaster oven in convection mode) (see below).

Let it stand for 5 minutes and serve (the first picture).

I was not sure the grated nagaimo and egg ratio but it came out ok. This is a sort of healthy Béchamel sauce substitute. The eggplant and avocado went well together. The next day, we placed the remaining dish in smaller individual ramekins and added a bit more cheese and toasted it in the highest setting. It heated up very nicely.