How to prepare pickled eggplants

Hi there
I believe you meant pickled eggplant and not marinated........ its 2 diffrenet things.
However, I have never heard of pickled eggplant  with beet. . Any way, you can find the 2 recipes (for pickled and marinated below)
 Pickled - this is the Middle eastern way:-
Use either 3 big eggplant or 1 Kg or the small one's. Wash eggplant and trim off stems and cube. Cook in boiling, lightly salted water for several minutes. Drain thoroughly.

Cook 1/2 Kg sugar, 3 cups vinegar and 1 tabs paprika together until mixture boils. Add eggplant cubes and 4 tabs mustard seeds, 2 tabs papper corns, 1 tabs ginger and bring to a boil and boil 3 minutes. Eggplant should hold cube shape. Put eggplant into jars and  cover with the pickling liquid. Seal and store up to 10 days before using.
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Marinated -
600 gr' small eggplants , trimmed and cut lengthwise
1 1/4 teas salt
5 tabs red-wine vinegar
1 teas sugar
1 garlic clove, sliced
1/4cup finely chopped fresh mint
1/2 cup olive oil


Toss eggplant with 1 teas salt in a colander set over a bowl, then let drain 30 minutes. Rinse eggplant, then drain, pressing gently to extract any excess liquid. Pat dry.
Whisk together vinegar, sugar, and remaining salt in a small bowl until sugar is dissolved. Stir in garlic and mint.
Heat oil in a nonstick skillet over moderately high heat until hot but not smoking, then fry eggplant, until cooked through . Transfer eggplant to paper towels to drain, then transfer to a large shallow dish. Spoon vinegar mint mixture over it. Marinate eggplant, covered and chilled, leave for  8 - 20 hours.
 
Hope that helps
Elinoar
http://www.cuisinemiddleast.com/recindex.html

 

I am pretty sure it is a Syrian or Turkish dish, If you want to make then red add a red pepper or beet as you please. 
Pickled Eggplant
8 baby eggplants, whole
1 medium onion, sliced
4 cloves garlic, diced
2 bay leaves
vinegar and water as required
Place the eggplants in boiling, salted water to cover. Cook over a high flame for 5 minutes. Remove, drain and transfer to sterile, large-mouthed, heat proof jars.
Add the remaining ingredients to the water and bring to a boil once again. Pour over the eggplants and seal the jars tightly. Let stand, exposed to light, for 7 days before serving. After opening, the pickles should be refrigerated.

 Vinegar is a matter of taste, I would recommend 2-3 spoons for about half a liter. You boil the eggplants in-order to get them soft around 5-8 minutes.

Here is an alternative recipe for a syrian stuffed pickled eggplant:

• 2 1/2 lb. baby eggplant (2 1/2 to 3 inches in length)
• 2 Tbsp Coarse Sea Salt
• 1 lb. finely-chopped walnuts
• 3 Tbsp Extra Virgin Olive Oil
• 1 clove garlic per eggplant
• 1/4 cup distilled white vinegar
• 1/4 cup water
• 1/4 cup beet juice (from a can of sliced beets is best)

Yield 1 quart.

Boil eggplant until slightly tender. DO NOT OVERCOOK. Drain, immerse in ice water to halt cooking. Remove eggplant from water when cool, and slice the side of each eggplant just enough to allow for stuffing.

Fill each eggplant with one piece of garlic, rub inside and outside with salt; stuff with the walnuts and place in the jar. Cover with water, oil, vinegar and beet juice.  Place in refrigerator for 1 week.