To a large pot of cool water, add 3 large pinches of salt. Slice a lemon in half and squeeze the juice into the water. Add the squeezed lemon halves and the 4 whole cloves of garlic. Add the potatoes and bring the water to a boil; boil lightly until the potatoes are fork-tender, 15 to 20 minutes. Drain the potatoes completely, allowing as much liquid as possible to drain off. Cool to room temperature.
Meanwhile, heat a large pan over medium-high heat and add olive oil to generously coat. Add the chopped garlic and saute until it just begins to soften but does not brown, 2 to 3 minutes. Add the potatoes cut-sides down in an even layer (you may have to do these in batches in order to not crowd the pan). Cook, flipping as necessary, until brown and crispy on all sides, about 8 minutes. Season with salt and red pepper. Add the oregano and the juice and zest from the remaining lemon. Stir to coat completely. Remove from the heat and serve!