Chop the mushrooms, and cook in 2 Tbs olive oil + 2 Tbs butter, with a pinch of salt.  In the first few minutes of cooking, as the mushrooms release their liquid, remove from the heat briefly, drain the mushroom broth, and reserve for later (you should get about 3/4 cup of liquid).  Return the pan back to the heat, and continue to cook for another 7-8 minutes, until the mushrooms are fully cooked.

Transfer the mushrooms to a food processor, fitted with the S-blade.  Add the rest of the pesto ingredients, and pulse a few times until you get a thick pesto consistency.  Taste and adjust the seasoning if needed.

Place 1 tsp of the mushroom pesto in the center of a won ton wrapper.   Moisten the edges with water, and place a second wrapper on top, pressing the edges to seal the filling.  Using a cookie cutter, press on the sealed ravioli to cut into shape.  I used a fluted-edge circle cookie cutter.   You can also use a fork to press on the edges.  

Bring a large pot of salted water to a gentle boil.  Add the ravioli in batches (without overcrowding the pot), wait until they float to the surface, and cook for two more minutes.  Remove with a slotted spoon.

Melt the butter in a small pan and add the sage leaves.  Cook on medium-to-low heat until the sage leaves get crispy, and the butter gets brown.  Remove the leaves to a plate.

To the butter in the pan, add the rest of the reserved mushroom broth, and the cream, and continue to cook until the sauce thickens.  Taste and adjust the seasoning.

Pour the sauce over the ravioli and serve with a generous shaving of Parmesan cheese, and the reserved crispy sage leaves.