On a large baking sheet, toss together the potatoes, lemon, 1 tablespoon olive oil and a generous pinch of salt. Place in the oven and roast for 20 minutes or until the potatoes are fork tender. 

Remove the lemon from the pan.  Use the back of a spatula or a fork to gently press down on the potatoes, smashing them to about 1/4 inch thickness.

In a small bowl combine 2 tablespoons olive oil, the garlic & oregano. Spoon the mixture evenly over the smashed potatoes.  Season to taste with salt and pepper. Sprinkle with the grated parmesan.  Return the potatoes to the oven and roast another 20-25 minutes or until golden and crisp. 

Meanwhile, finely chop half or all of the roasted lemon (peel and all) and add to a small bowl along with the remaining 2 tablespoons olive oil, the basil, and a pinch of salt. 

Transfer the potatoes to a serving dish.  Drizzle the potatoes with the lemon mixture and serve with sliced feta.