Frozen premade dumplings wrappers, sold as wonton skins or gyoza skins, are natural for making ravioli. You can stuff endless things inside them - just make sure it is a uniform mixture that sticks together but is not too wet. Leftover mashed potatoes, mixed with garlic and maybe cheese, would be fabulous. I just made ratatouille from a big gorgeous pile of vegetables bought at H&W produce (where eggplants are 79 cents each right now) and made ravioli with the finely chopped leftovers. Am also planning to try a mung bean puree.
For another filling, I used homemade goat's milk ricotta, spinach, green onion, garlic, and oregano. The onion and garlic are precooked a bit so when the ravioli are boiled they are cooked through at the same time as the more delicate spinach. I enjoyed these most with no more than olive oil, salt, and pepper. The spicy tomato sauce I originally tried drowned out the delicate flavour of the cheese. If cooking for kids or someone extremely averse to goatiness, slosh on the tomato sauce.
For the herbed cheese ravioli filling: 3 green onions and two garlic cloves, chopped and cooked til soft; 1 1/2 cups homemade ricotta; 2 handfuls spinach leaves, julienned; generous dusting of dried oregano; 1 lb dumpling skins. Combine filling and taste for salt, then make into ravioli. I did them in the same shape as the mandu, though you can make big square ones by using two skins per raviolo. Freeze in single layer before putting into a freezer bag and use within a couple months.
Many food bloggers have posted on making cheese, so I will not go into details on this rather than to note that my best flavour/texture results have come from using a slow cooker on high to heat the milk and lemon juice for the acid. I also don't have a thermometer; just wait for the curds to form.