Bring a covered medium pot of water to a boil over high heat. Add the beets and cook, uncovered, at a medium boil for about 20 minutes until fork-tender. Drain and set aside.
Place the lettuce, onion, carrot, cranberries, garlic, and oregano in a salad bowl.
Using two wooden spoons, toss to combine. Drizzle the walnut and olive oils evenly over the salad, then toss gently to coat. Drizzle the vinegar and the honey evenly over the salad, sprinkle with salt and pepper, then toss to combine. Taste for seasonings. Scatter the crumbled feta and the pecans evenly over the top. Serve immediately.