Begin by prepping your ingredients. Peel the potatoes, carrots and beets and then cut them into small 1 inch cubes. Finely dice the onions, celery, red pepper, garlic and cilantro.
Set two pots with water on the stove. Add the potato and carrots to one pot and the beets to the other pot. They are separated since the beets will stain the water red. Bring the water with the vegetables inside to a boil, waiting until the vegetables are cooked through. You want them to retain their firmness. Be careful not to overcook them or they will turn to mush when you mix the salad together. They will cook quickly, approximately 8-10 minutes, since they are cut into small cubes, although you should poke with a fork to test for doneness.
While the vegetables cook, take a frying pan and sauté the onions, red peppers, celery and garlic in olive oil on medium high heat. Continue to sauté until the onions turn a golden brown.
Once the vegetables are cooked strain the water and put them all in a large mixing bowl. Add in the sautéed ingredients and stir together with a wooden spoon.
Hard boil the eggs by placing them in boiling water. Once cooked place them in an ice bath then peel the shell off.
Add in the mayonnaise, white vinegar, cilantro and stir. Dice the hard boiled eggs and add to the salad. Add salt and pepper to taste.