Rinse the eggplant, dry with paper towels, slice about 3/8 inch thick.
Preheat a large skillet over medium heat. Add 1 tablespoon of olive oil. Place about 1/3 of sliced eggplant on the skillet in one layer and cook over medium heat for about 6 minutes, until golden brown. Flip on the other side and continue cooking for another 6 minutes. As eggplant really soak in oil when they are cooking, add about 1 teaspoon of olive oil when flipping. Transfer to a platter lined with paper towel to remove excess oil and cool down. Repeat this step until all eggplant slices are cooked (2 large eggplant are usually cooked in 2-3 batches, depending on the size of the skillet you are using).
Spread a bit of pressed garlic over the top of each eggplant slice.
Grab a container with a tight lid, spread a pinch or two of pressed garlic on the bottom and sprinkle some chopped dill and parsley.
Place a layer of eggplant slices making sure they don't overlap or barely overlap. Sprinkle a tiny pinch or two of salt, grind some black pepper to taste. Finish the layer by sprinkling some chopped dill and parsley. Repeat until all vegetables are layered. Finish with a pinch of salt, pepper and chopped greens.
Cover with with a lid and keep at room temperature for 4 hours before serving.
Marinated eggplant can be refrigerated for up to 7-8 days. You can serve it cold or brought to room temperature before serving.
If you want to reduce the harsh taste of raw garlic, zap the cloves in a microwave oven for 10 seconds or blanch in boiling water for a minute before pressing.