Preheat the oven to 375 degrees F.
In a large mixing bowl, add the potato cubes and season with 2-3 tablespoons of olive oil, ½ teaspoon salt, ½ teaspoon pepper, ½ teaspoon garlic powder, ½ teaspoon paprika, ¼ teaspoon oregano, and ¼ teaspoon cayenne (optional). Toss to coat well and evenly spread potatoes onto a parchment-lined baking sheet. Set the seasoned bowl aside as you will use it for mixing.
Roast until tender and golden for 20-30 minutes or until potato pieces are fork tender. The baking time will depend on the size of the potato pieces. When cooked through, remove from the oven and let cool for 20 minutes.
In the same bowl you used to season potatoes, combine yogurt, lemon juice, minced garlic, chives, and dill—season with additional salt and pepper. Scrape down the sides of the bowl so the dressing is at the bottom.
On top of the dressing, place the sliced red cabbage, cucumbers, and green onions.
Once potatoes have cooled, add them to the top of the mixing bowl and toss all ingredients until well combined. *This can be made ahead to this point and refrigerated until ready to serve.