Make balsamic onion jam. Heat oil in a large saute pan over medium heat. Add chopped onion and saute until browned, about 10-12 minutes, stirring occasionally.
Add water, brown sugar, balsamic vinegar, mustard seeds, salt, and pepper, stirring to combine. Reduce heat to low and continue to simmer for 40-45 minutes or until onions are dry, stirring occasionally. Remove from heat and let cool completely.
Preheat oven to 375 degrees F. Line a baking sheet with parchment paper.
Cut puff pastry sheet into 4 equal portions. Cut each quarter in half lengthwise, then cut each portion in half again diagonally. You should have 16 triangles total.
Cut each slice of cheese into 4 quarters. Place 1 teaspoon onion jam on the wide end of each triangle. Top with 1 cheese square and 1 cocktail wiener, then roll up. Put pig in a blanket seam side down on prepared baking sheet. Repeat with remaining ingredients.
Brush pigs in a blanket with egg wash and sprinkle with flaky sea salt and coarsely ground black pepper. Bake for 20-25 minutes or until puffed and golden, rotating the baking sheet halfway through baking. Serve hot.
Notes
The balsamic onion jam can be prepared up to 1 week in advance.