If aging the duck breast, set it skin side up on a plate and refrigerate uncovered for at least 4 days and up to 7.
Preheat the oven to 400°. Put the beets in a baking dish and drizzle lightly with olive oil; cover with foil and roast until just tender, about 1 hour. When the beets are cool enough to handle, peel and slice them into 1/4-inch-thick rounds.
Meanwhile, in a large, ovenproof skillet, cook the bacon over moderate heat until crisp, about 5 minutes. Using a slotted spoon, transfer the bacon to paper towels to drain. Add the bread to the skillet and stir well to coat with the bacon fat. Transfer the skillet to the oven and bake, stirring a few times, until the bread is crisp, about 15 minutes. Season lightly with salt and pepper.
If using bone-in duck breast, remove the breast halves from the bone. Trim the skin to just cover the meat. Heat a medium skillet until hot. Season the duck breasts with salt and pepper and cook skin side down over moderate heat until the skin is richly browned and crisp, about 12 minutes. Turn the duck and cook until medium-rare, about 4 minutes longer. Transfer the duck to a carving board and let rest for 5 minutes. Slice the duck breasts crosswise 1/8 inch thick.
In a large bowl, toss the beets with the bacon, croutons, tomatoes, scallions and oregano. In a small bowl, stir the 1/4 cup of olive oil with the vinegar and season with salt and pepper. Pour the dressing over the salad and toss well. Mound the salad on plates, top with the sliced duck and serve.