1. Bring a large pot of salted water to a boil over high heat. Prepare an ice-water bath and set aside. Add spinach to boiling water and cook until bright green and tender, about 1 minute. Drain and immediately transfer to ice-water bath to cool; drain and, using your hands, squeeze as much liquid out of the spinach as possible.

2. Coarsely chop spinach and transfer to a large bowl. Add ricotta, 1/2 cup Parmigiano-Reggiano cheese, eggs, and nutmeg; mix until well combined. Season with salt and pepper and set filling aside until cool.

3. Line a baking sheet with parchment paper and lightly dust baking sheet and work surface with flour; set baking sheet aside. Place 1 sheet of pasta on prepared work surface and trim to a 6-by-18-inch rectangle. Cut rectangle in half horizontally and then vertically into 3-inch strips to make 12 squares. Repeat process with remaining pasta sheets.

4. Place 1 tablespoon of filling in the center of one pasta square. Lightly brush edges with water and cover with a second pasta square. Press down on pasta squares to seal, making sure to press out all of the air; trim edges with a fluted cutter and transfer to prepared baking sheet. Repeat pasta with remaining filling and pasta squares to make tortelli.

5. Meanwhile, melt 1 tablespoon butter with olive oil in a medium skillet over medium heat. Add squash and cook until softened. Remove from heat and set aside.

6. Bring a large pot of salted water to a boil. Add tortelli to boiling water and cook until they rise to the surface, 2 to 3 minutes.

7. In a large skillet, melt remaining 4 tablespoons butter over medium-high heat. Continue cooking until butter just turns golden brown. Remove from heat and add sage leaves.

8. Drain tortelli, reserving 1 cup pasta cooking water. Add tortelli and squash to skillet and toss to coat, adding pasta water, 1 tablespoon at a time, as necessary. Sprinkle with cheese and drizzle with balsamic vinegar. Season with salt and pepper; serve immediately.