Cut the eggplants in half. With a spoon, gently scoop out the inside meat of the eggplants, being careful not to tear the skin. Save the eggplant meat in a bowl. Sprinkle salt on the inside of the scooped-out eggplants and let them sit for about 20 minutes.

Preheat the oven to 350 degrees. In a pan, begin sauteing the onions on medium-low with about two tablespoons of olive oil.  

Place the eggplant meat and basil leaves and tomato in a food processor until finely chopped, or chop these very finely by hand. Add this mixture to the onions and cook for about 5 minutes. 

In a medium-sized bowl, combine the eggplant mixture with bread crumbs, egg, a little more salt, and parmesan cheese. Mix together completely. 

Spoon the mixture into the scooped-out eggplants. Top the stuffed eggplants with a little more cheese and bake for about 20-25 minutes.