Preheat your oven to 400°F (200°C).
In a pot of salted boiling water, cook the diced butternut squash until fork-tender, about 10-12 minutes.
Drain the squash and puree it in a blender or food processor.
In a large skillet, heat the olive oil over medium heat and sauté the minced garlic until fragrant.
Add the pureed butternut squash to the skillet and season with salt and pepper. Cook until heated through, about 5 minutes. Set aside.
On a floured surface, roll out the ravioli dough to about 1/8 inch thickness. Cut into squares using a ravioli cutter or sharp knife.
Place a teaspoon of the butternut squash mixture onto half of the dough squares, leaving about 1/2 inch of space between them.
Top each filled square with another square of dough and use a fork to press the edges firmly together to seal the ravioli.
Place the ravioli on a parchment paper or silicone baking mat-lined baking sheet and bake for 15 minutes, or until golden brown.
In the meantime, make the brown butter sauce. Melt the butter in a large skillet over medium heat. Cook, stirring occasionally, until the butter turns a golden brown color and has a nutty aroma, about 5-7 minutes.
Remove the skillet from heat and strain the butter through a fine-mesh strainer into a large mixing bowl. This will remove any solids and leave you with a smooth brown butter sauce.
Add in the grated parmesan cheese and stir until melted.
Season with salt and pepper to taste.
Serve the ravioli hot, topped with the warm brown butter sauce and fresh sage leaves, if desired.