The squash and onion mixtures can be cooked in advance and refrigerated for up to three days. Assemble the galette just before baking.
Preheat oven to 450 degrees. Melt butter with honey in a small saucepan over medium heat. Arrange squash rounds in a single layer on a rimmed baking sheet, and brush both cut sides with butter-honey mixture. Season with salt and pepper on both sides. Roast until squash rounds are browned on bottoms, about 15 minutes. Remove from oven. Reduce heat to 375 degrees.
Meanwhile, heat oil in a large saute pan over medium heat. Add onion, and cook, stirring occasionally, until caramelized, about 20 minutes.
Turn out pate brisee onto a lightly floured surface. Roll dough into a 16-inch round, about 1/4 inch thick. Refrigerate for 15 minutes.
Stir together ricotta and 2 eggs in a medium bowl. Season with salt and pepper.
Spread ricotta mixture over dough, leaving a 1-inch border. Top with onions and squash rounds. Sprinkle with sage leaves, and season with pepper. Fold dough over edge of filling to form a crust. Brush crust with egg wash. Bake until golden brown, 50 to 60 minutes. Serve warm.