Moussaka from Lebanon (地中海茄子)

Over the weekend we went to Old Town Monrovia, to see Arrival, an interesting Sci-Fi movie.  After the movie, we strolled into a new Mediterranean restaurant nearby, and fell in love with this vegetarian appetizer, Mousakah (how it's named on the menu).  It's served as a cold dish, along with warm pita bread.  As it turns out, what we had in the restaurant was a streamlined version of the dish known as Moussaka from Lebanon (how it's named online), vs the Greek Moussaka, an eggplant casserole dish.  We tried to recreate the restaurant version of this dish and patterned our recipe below after two online recipes (1 and 2), but we left out the chick peas and oven baking.  We also followed the restaurant owner's suggestion of using vegetable oil, in place of olive oil.  The result is quite satisfying!  BTW, it's easy and quick to make this dish.

1. [Prepare the ingredients] Rinse and cut 3 Chinese Eggplants (or 1.5 regular eggplant) into ~1/2" cubes.  Slice 6-8 cloves of garlic.  Slice 1 large (or 2 smaller) onions (1/2"- 1" long slices).  Cut 1 green bell pepper (or half a green and half a red bell pepper) into ~1" long slices. Dice 1-2 tomatoes (into 1/2" cubes).  Note- Regular eggplant might take longer to cook.  
2. Add 1-2 Tbsp of veggie oil into a saute pan, add 1/4 tsp salt, turn on medium-to-high heat, pour in the eggplant cubes, stir, mix, and cook till it's almost soft (4-5 minutes). Take the eggplant cubes out and set aside.  Note- As the main ingredient for this dish, eggplant's texture is the key to this dish's success. Don't overcook eggplant at this point (if not sure, under-cook it).  If under time pressure, conduct this step at the end of Step 3.
3. Add 1-2 Tbsp of veggie oil into the same saute pan, turn on medium-to-high heat, add the garlic and stir till fragrant.  Add the onion and stir till almost translucent (2-3 minutes).  
4. Add bell pepper and cook for another 2-3 minutes. Add tomatoes.  Now, season with 1/2 tsp salt, 1/4 tsp black pepper, 1/2 tsp of paprika, and 2 Tbsp of tomato paste.  Stir and mix evenly.
5. Add the almost-cooked eggplant into the pan.  Add 1/2 cup of water.  Stir and cook till the eggplant cubes are soft, but not mushy (2-3 minutes for Chinese Eggplant, maybe longer for regular eggplant).  Turn off heat, season to taste with salt, pepper, and paprika. 
6. Chill and serve as a cold dish, with warm pita bread.  See picture below for the outcome in our kitchen.