Eggplant and green tomato on the grill

I have a wonderful variety of eggplant called Dancer. Violet colored, medium size, and the tastiest ever. It has been producing all spring summer and fall. Planted 1 seed in a pot and it has produced enough eggplant for me and my wife from May to December.  I grilled some last night that was great. I have some green tomatoes in the garden also. I am thinking about grilling both the green tomatoes and eggplant, putting some cheese on the eggplant and then topping with a green tomato. I will post how it turns out.