Whisk together the milk, Parmesan, salt, pepper, parsley, and eggs.
Heat a large skillet over medium heat and add a little olive oil. Add the garlic and cook, stirring, until fragrant. Add the leftover spaghetti, pour over the egg mixture, and cook, without stirring, until the bottom is browned, about 5 minutes.
To flip the pie, set a plate the size of the skillet on top. Invert the skillet so the pie falls on to the plate. Invert the pie onto another plate, cooked-side up. Return the skillet to the medium-high heat, add a little more oil, and slip in the pie. Continue cooking until the bottom is browned, about 5 minutes more.
Transfer the pie to a plate, cut into wedges, and serve.