01 - Heat olive oil in a large skillet over medium heat. Add sliced onions, sugar, and salt. Cook, stirring regularly, for 15 to 20 minutes until onions reach a deep golden color and soft texture. Stir in balsamic vinegar and continue cooking for 2 minutes. Allow to cool completely.
02 - Preheat oven to 400°F. Line a baking sheet with parchment paper.
03 - In a large mixing bowl, combine the sausage meat, dried thyme, Dijon mustard, ground black pepper, salt, and cooled caramelized onions. Mix until ingredients are evenly blended.
04 - Roll out puff pastry on a lightly floured surface into a 12 x 10 inch rectangle. Cut lengthwise into two equal strips.
05 - Divide the sausage filling in half. Shape each half into a long log down the center of each pastry strip.
06 - Brush one long edge of each pastry strip with beaten egg. Fold pastry over sausage filling to enclose, pressing edges to seal. Place each roll seam-side down.
07 - Cut each filled pastry log into 8 equal pieces. Transfer to the prepared baking sheet, spacing evenly. Brush tops with remaining egg wash, and sprinkle with seeds if desired.
08 - Bake for 20 to 22 minutes, until pastry is puffed and golden brown and filling is fully cooked.
09 - Allow sausage rolls to cool briefly before serving warm or at room temperature.