How to Make It
In a small bowl, mix the mayonnaise with the ketchup, lemon juice and Worcestershire sauce. Season the sauce with Tabasco and salt and pepper.
In a large nonstick skillet, heat the oil until almost smoking. Add the sliced onion and cook over moderate heat until softened, about 3 minutes. Add the beet slices and cook until almost tender, about 5 minutes. Stir in the carrots and cook for 5 minutes. Add the potato, season with salt and cook until all of the vegetables are tender, about 7 minutes.
In a medium bowl, beat the eggs with a dash of Tabasco; season with salt and pepper. Gently stir the eggs into the vegetables, cover and cook over moderate heat until the eggs are just barely set, about 5 minutes. Flip the vegetable omelette with a spatula and cook for 1 minute longer. Transfer the omelette to a work surface, cover loosely with foil and keep warm.
Meanwhile, lightly toast the bialys. Spread the sauce on the bialys. Cut the vegetable omelette into 4 wedges, set a wedge on each bialy, close the sandwiches and serve.