Preheat oven at 400 degrees Fahrenheit (200 C).
Wash the eggplant and slice about ¼ inch thick, place in colander and salt them, set aside.
Slice the peppers in thin rings, set aside.
Slice onion in thin rings and add to the peppers.
Rinse and dry the eggplant and place the eggplant, peppers, onions, garlic and olive oil in large bowl and toss.
In a small bowl mix the tomato paste with 3 tablespoons of water and mix. Add this to the vegetables and mix well until all vegetables are coated with tomato paste and olive oil.
In a casserole dish place half of the vegetables in one layer, sprinkle with half of the mitzithra and half of the kefalograviera. Repeat for a second layer.
Cover the casserole dish with aluminum foil and bake for about 40 minutes.
Remove the aluminum foil and bake for another 5 minutes until the cheese bubbles.
This is enjoyed warm or cold and goes well with Greek yogurt.