Step 1: Preheat your oven to 400°F (200°C).
Step 2: In a large mixing bowl, combine the cubed potatoes, 1/4 cup olive oil, lemon juice, lemon zest, minced garlic, oregano, salt, and black pepper. Toss well to ensure all potato pieces are evenly coated.
Step 3: Spread the seasoned potatoes in a single layer on a large baking sheet. Roast for 25-30 minutes, or until the potatoes are fork-tender and beginning to turn golden brown at the edges.
Step 4: While the potatoes are roasting, wash and de-stem the kale. Chop the kale into bite-sized pieces. In a separate bowl, massage the kale with a tiny drizzle of olive oil and a pinch of salt for 1-2 minutes until slightly softened.
Step 5: After the initial potato roasting time, remove the baking sheet from the oven. Add the massaged kale to the baking sheet, spreading it among the potatoes. Return to the oven for another 5-10 minutes, or until the kale is slightly wilted but still vibrant.
Step 6: While the kale finishes cooking, heat 1-2 tablespoons of olive oil or butter in a non-stick skillet over medium-high heat. Crack the eggs into the hot oil, making sure they don't touch. Cook for 2-3 minutes, basting the whites with hot oil, until the edges are crispy, the whites are set, and the yolks are still runny.
Step 7: Remove the baking sheet from the oven. Crumble the feta cheese generously over the warm potatoes and kale. The residual heat will slightly melt and soften the feta.
Step 8: Divide the Greek Lemon Potatoes with Kale and Feta among four serving plates. Top each portion with one or two crispy fried eggs. Garnish with fresh parsley or dill, if desired, and a final squeeze of fresh lemon juice. Serve immediately and enjoy!