Thinly slice onions and melt butter in a large saute pan over medium heat. Add sliced onions to the pan and cook until they begin to sweat. Season with a pinch of salt.
Reduce the heat to medium low and continue to cook onions until the are golden brown and caramelized, stirring occasionally and adding splashes of water as they get dry and begin to stick to the bottom of the pan. This will take about 40 minutes.
When the onions are almost done, soak the prunes in hot water for about 10 minutes. Drain and finely chop. Add the chopped prunes to the onions and cook for another 2-3 minutes until everything is well incorporated. Remove from heat and set aside.
Preheat the oven to 425 degrees f.
Lay out a large sheet of parchment paper on the counter and dust with all purpose flour. Roll out the thawed puff pastry into a rectangle about 10X15 inches or roughly double the size. With a paring knife, gently trace a half inch border around the edges, being careful not to cut through the pastry. Use the parchment paper to slide it onto a rimmed baking sheet.
Spread an even layer of cheese inside the border of the puff pastry. Top with the caramelized onion and prune mixture and use a spoon to spread it out into an even layer.
Thinly slice the pears and arrange on top of the cheese and onion mixture.
Brush the edges of the tart with egg wash.
Bake the tart at 425 degrees f for about 20 minutes until the edges are golden brown and puffed.
Let cool for 5-10 minutes before slicing and serving.
Notes
Caramelized onions can be made 3-4 days ahead of time. Store in the refrigerator in an airtight container and let them come to room temperature before assembling the tart.