Preheat the oven to 425 degrees F. Place the sliced potatoes on half of a baking sheet. Toss with 1 tablespoon of olive oil and salt and pepper. Make a foil tray with sides on the other half of the baking sheet and lay the pieces of bacon inside (to contain the grease).
After about 15 minutes, if the bacon has browned and cooked (no longer pink) carefully remove the foil tray (without spilling the hot grease!) and place the potatoes back in the oven until tender when pierced with a fork, another 5 or 10 minutes. Crumble the bacon when it's cool enough to handle and set aside.
For the mushrooms
Meanwhile, heat the remaining 2 tablespoons of olive oil in a small skillet over medium-high heat. Add half of the sliced red onion and cook while stirring occasionally until it begins to soften and brown, about 2 to 3 minutes.
Add the mushrooms and garlic and cook until the mushrooms release their liquid and then begin to brown, 4 to 5 minutes. Stir in oregano, season with salt and pepper, and remove from heat.
For the salad
Arrange the chopped lettuce on a large platter. Sprinkle the ingredients over top including the potatoes, bacon, mushrooms, remaining raw onion, eggs, and feta. Season with salt and pepper. Vigorously shake dressing to emulsify, drizzle over top, and serve.