Whisk the ricotta, spinach, prosciutto, egg yolks, salt, and pepper in a medium bowl to blend.
Place 1 tablespoon of the ricotta filling in the center of a wonton wrapper. Brush the edge of the wrapper lightly with water. Fold the wrapper in half, enclosing the filling completely and forming a triangle. Pinch the edges to seal. Transfer the ravioli to baking sheets. Repeat with the remaining filling and wrappers. (Can be prepared up to 2 hours ahead; cover and refrigerate.)
Melt the butter in a heavy small skillet over medium heat. Add the oregano and stir 1 minute. Season, to taste, with salt and pepper. Remove from the heat.
Working in batches, cook the ravioli in a large pot of boiling salted water until just tender, stirring occasionally, about 4 minutes per batch. Transfer the ravioli to a large shallow bowl.
Pour the oregano butter over the ravioli and toss gently to coat. Sprinkle the pecorino over the ravioli and serve.
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