Preheat the oven to 200ºC. Wash and dry the peppers and eggplants. Place in the oven with the onion. Roast for 20 minutes.
Turn the vegetables over and add the two garlic cloves. Leave in the oven another 10 minutes. Remove and set aside.
Peel the roasted garlic and crush in a mortar. Add the olive oil and mix well.
Heat the balsamic vinegar and honey in a small saucepan. Reduce to a simmer about 5 minutes or until it acquires syrup texture. Set aside.
Remove the skin from the peppers and eggplants, and cut them into strips. Salt lightly. Gratin the cheese slices in the oven for about 5 minutes at 180ºC.
Put the roasted vegetables on plates, adding the olive oil and roasted garlic, crowning the vegetables with a slice of cheese. Garnish with balsamic vinegar reduction and serve.