In a large mixing bowl, whisk the eggs with the yogurt and half a teaspoon of kosher salt.
Peel and dice the potatoes. Peel and mince the red onion. Clean the mushrooms and cut them into bite-sized pieces (about four pieces for small mushrooms or 6-8 pieces for medium-sized mushrooms).
Turn the oven on to 390°F (200°C or 180°C fan) and let it preheat.
To an ovenproof large pan, over medium-high heat, add 2 tbsp of olive oil. Once the oil is hot, add the potato cubes and cook for about 10 minutes, stirring occasionally.
To the same pan, add two tablespoons of unsalted butter, mushrooms, onions, lemon juice, half a teaspoon of kosher salt, a quarter of a teaspoon of black pepper, and half a teaspoon of dried oregano. Keep cooking, stirring from time to time, until the mushrooms and potatoes are soft and cooked through (about 10 minutes).
Remove the pan from the heat and add the beaten egg mixture, distributing it evenly with a spatula.
Top with crumbled feta.
Place the ovenproof pan in the oven and bake the frittata at 390°F (200°C or 180°C fan) for about 15-18 minutes until it’s cooked through and golden on the edges and the top.