In a small bowl, combine canned pumpkin puree, 1/3 cup grated Parmesan (or Romano or Asiago) cheese, cayenne if using, and salt and black pepper to taste. Set aside.
Place 12 wonton skins on a flat, non-stick surface lightly dusted with all-purpose flour. Divide the filling equally, placing approximately 1 tablespoon in the center of each wonton skin.
Brush around the outside of the filling with beaten egg. Carefully place another wonton skin over the filling. Gently stretch it to make the edges come together neatly, removing any air pockets from the ravioli. Repeat until 12 ravioli are assembled.
Bring a saucepan of salted water to a boil. Add olive oil.
Place the butter in a saucepan or skillet over medium heat. When the butter has melted and begins to simmer, reduce the heat to low and let it continue simmering until it starts to turn a light golden brown.
Add the sage leaves and cook for 1-2 minutes, being careful the butter does not get overly browned or burned. Remove from heat and set aside. Remove sage with a slotted spoon and drain on a paper towel. (Try not to take too much butter with the leaves.)
Working in batches, place 4 ravioli in the boiling water. Cook for 2 minutes or until they begin to float slightly (they don’t need to come all the way to the top as they will cook quickly).
Remove with a slotted spoon and drain in a colander. Repeat with remaining ravioli.
To serve, place ravioli on a plate. Drizzle with browned butter, leaving any browned milk solid bits behind in the saucepan. Top with sage leaves (both cooked and slivers), Parmesan (or Romano or Asiago) cheese and pecans. Serve immediately.