Coat a 12-inch nonstick saute pan with 3/4 cup oil, add the leeks to the pan, season with salt and bring to a medium heat. Cook until the leeks are starting to soften and are very aromatic, 5 to 6 minutes. Toss in the potatoes, season with a little more salt and the crushed red pepper, about 3 minutes. Add the ham and the remaining 1/4 cup of oil. Cook, stirring occasionally to be sure the potatoes do not stick to the bottom of the pan, until the potatoes start to soften, 15 to 18 minutes.
Meanwhile, beat the eggs with about 2 tablespoons water to a smooth consistency in a bowl, then add a heavy pinch of salt and half the grated cheese and beat together until the eggs and cheese are a smooth, homogeneous mixture.
Using a colander or mesh strainer, carefully strain out the excess olive oil from the potato-leek mixture and reserve. Return the potato-leek mixture to the pan and stir in the eggs. Cook over medium heat, stirring occasionally, until the eggs start to cook around the outside edges of the pan. Transfer the pan to the oven and bake until the eggs are cooked through, about 18 minutes.
Remove the pan from the oven. Place a snug fitting lid or a baking sheet on the pan, then hold the handle of the lid, swing the pan and flip the frittata onto the pan lid. Commit to it! It's fun! Slide the frittata onto a plate. You can serve this hot or at room temperature.
Toss the mixed greens with the red wine vinegar, 2 tablespoons of the reserved potato-leek oil and a pinch of salt in a bowl. Serve with slices of the frittata.