Preheat oven to 375°F. Wrap beets in aluminum foil and set on a baking pan. Roast for 60 minutes, or until a knife easily pierces the beet. Set aside to cool.
While beets are cooling, put on a pot of salted water and bring to a simmer. While you are waiting for the water to come to a simmer, prepare the ice bath: fill a large bowl with cold water and ice. Set aside.
Add green beans, peas and shredded cabbage to the simmering water and cook for 4 minutes. Remove from water with a slotted spoon or a spider (don't throw out the water) and plunge the bean mixture into the ice bath.
Add carrots and cook for 5 minutes, then add cauliflower to the carrots. Let them cook for a few minutes more until softened. The goal is to soften the vegetables, they should still have a little resistance when you bite them. When carrot and cauliflower mixture is to your liking, drain and add to ice bath.
Remove all the vegetables from the water and set aside on clean kitchen towels to drain completely.
When beets have cooled enough to handle, peel them by rubbing the outside with your hands or a paper towel and the skins will slip right off. (I suggest wearing gloves while you do this, otherwise your hands will be purple for a week!)
Dice the beets into small pieces, and add all of the vegetables to a large, non-aluminum bowl. Add the oregano, vinegars, sugar and 1 - 2 teaspoons of salt, mix to combine and refrigerate.
Stir vegetable mixture after an hour or so to ensure everything has soaked in the vinegar.
Taste vegetables and adjust seasoning if needed. Stir again, pack into containers and refrigerate.