If you like to make fresh pasta dough, make a batch and roll it out for these ravioli. Alternatively, buy fresh pasta sheets, then roll them slightly thinner, and cut them into strips to form individual ravioli. Store-bought wonton wrappers make this recipe even easier for anyone who doesn't have a lot of time to spend in the kitchen.
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In a small frying pan, melt the butter over medium heat and heat until it just begins to brown, 2-3 minutes. Add the sage and crisp in the butter for 30 seconds. Remove from the heat and season with the salt. Set aside and keep warm until ready to serve.
Position a rack in the center of the oven and preheat to 425 degrees.
Rub the cut sides of the sweet potatoes with the oil. Place cut side down on a rimmed baking sheet and roast until very tender when pierced with a fork, 30-45 minutes. Set aside until cool enough to handle. Scoop the flesh into a bowl, discarding the skins. Use a potato masher, ricer, or food mill to mash the potatoes until completely smooth.
In a small frying pan, melt the butter over medium heat. Add the garlic and sauté until soft but not brown, about 1 minute. Add the sage and crisp in the butter for 30 seconds. Remove from the heat and stir in the salt and pepper. Add to the sweet potatoes in the bowl and mix to combine.
Line a baking sheet with parchment paper. On a clean work surface, arrange 8 wonton wrappers in a row. Keep the remaining wrappers covered with a damp paper towel to prevent them from drying out. For each raviolo, measure a level 1 tablespoon of the filling and mound it in the center of a wrapper.
Lightly brush the edges of the wrapper with water to moisten them. Place another wonton wrapper on top and gently press around the filling to release any air pockets. Using a 2 ¾-inch round biscuit cutter or fluted cookie cutter, cut out the raviolo and crimp the edges. As the ravioli are formed, transfer them to the baking sheet. Repeat to make the remaining ravioli.
Bring a large pot of salted water to a boil and gently add the ravioli. Reduce the heat so the water boils gently (otherwise the ravioli could split apart) and cook until tender, 4-5 minutes. Using a large slotted spoon or a wire skimmer, transfer the cooked ravioli to individual warmed plates or shallow bowls. Spoon the sauce over the ravioli and finish with a generous sprinkling of pecorino. Serve immediately.