Prepare the pasta water. Bring a pot of water to a boil, adding a pinch of salt.
Cook the pancetta. While the water heats, add the pancetta to a large skillet over medium heat. Sauté for approximately 3 minutes, until lightly browned. Remove the pancetta with a slotted spoon and set aside in a small dish. Pour off the excess rendered fat, leaving just a light coating of drippings in the skillet. Do not wipe the pan clean.
Wilt the arugula. Add the olive oil and arugula to the same skillet. Cook over medium heat until the leaves are wilted. Divide the arugula between two serving plates and set aside.
Cook the ravioli. Add the ravioli to the boiling water and cook for approximately 4 minutes, or according to package directions.
Prepare the brown butter sage sauce. While the ravioli cooks, add the salted butter to the skillet without wiping it clean. Allow the butter to melt and slowly brown over medium-low heat, stirring or swirling occasionally. Watch for golden-brown milk solids and a nutty aroma.
Add the garlic and sage. Reduce the heat to low and add the minced garlic and chopped sage leaves. Cook for 1–2 minutes, until the garlic is fragrant and the sage becomes slightly crispy.
After the garlic and sage have cooked for 1–2 minutes, squeeze the juice of half a lemon into the brown butter sauce. Stir gently to combine before adding the cooked ravioli.
Combine the ravioli and sauce. Drain the cooked ravioli and gently transfer it to the skillet. Toss carefully to coat the ravioli in the brown butter sage sauce.
Return the pancetta. Using a spoon, transfer the pancetta from its dish into the skillet, leaving behind any accumulated grease. Gently combine with the ravioli and sauce.
Serve. Divide the ravioli and pancetta between the two plates, spooning them over the wilted arugula. Drizzle with the remaining brown butter sauce and finish with freshly grated Parmesan cheese.