Preheat the oven to 425 degrees F. Line a baking sheet with parchment paper. Unfold the pastry sheet on the parchment. Lightly score the edges with a knife, leaving about a 1/2-inch border around the square. Brush the edges with the beaten egg, then set the egg aside. Prick the center of the pastry thoroughly with a fork, then refrigerate until ready to use.

In a skillet set over medium heat, cook the sausage until it's just browned throughout, about 5 minutes. Remove sausage from skillet but retain half of the grease. Reduce heat to medium-low, then add the butter and oil to the skillet and swirl. When melted and shimmering, caramelize the onion rounds for about 8 minutes on each side until they're a dark golden brown.

In a medium bowl, combine remaining egg, ricotta cheese, thyme, rosemary, 1/2 tablespoon of the sage, and salt and pepper to taste. Mix until combined.

Remove pastry from refrigerator. Spread ricotta mixture on top within the 1/2-inch border. Top with caramelized onions, sliced apples, and cooked sausage. Bake for 18-20 minutes, until the outer edge of the pastry is golden brown and cooked through. Garnish with remaining fresh sage when ready to serve.