Besides coring and chopping the tomatoes, cut the eggplants in half lengthwise and grate the Parmesan cheese.
Preheat the grill to a medium hot temperature. This will vary widely depending on whether you are cooking with gas or charcoal, the size of the grill, the Btu's, etc. The eggplant will take about 30 minutes so depending on your grill, plan accordingly. It's hard to explain just exactly how to grill anything because every grill is different. All I can say is the more you grill the more you will get a feel for how to use it most effectively. Practice, practice, practice and check out my grilling tips on my web site.
Place the chopped tomatoes along with the olive oil, butter and bay leaf in a small sauce pan and simmer over medium heat until the tomato breaks down to a saucy consistency. Be sure to stir during this process that should take about 15 minutes.
Remove the pan from the heat and season with salt and pepper. Remove and toss the bay leaf.
Next we want to toss the eggplant halves in the grapeseed oil with a little salt and pepper.
Grill the eggplant skin side down with the cover until the skin begins to char and the juices "boil up through the flesh and the flesh is tender." This should take about 25 minutes.
Using tongs to hold the eggplant, make an indentation in the flesh with the back of a spoon. Add a generous tablespoon to the tomato sauce into each indentation.
Cover and grill for an additional two minutes. If there is extra sauce, save it and serve it on the side at the table.
Now sprinkle each eggplant with a tablespoon of Parmesan cheese, cover and cook until the cheese begins to melt, about 2 minutes.
Remove from grill and serve it immediately with main course.