Thaw the puff pastry in the refrigerator. Keep the pastry very cold in the fridge right until you're ready to use it.

Place the peeled and chunked potatoes in a large pot. Fill with water to cover the potatoes. Bring to a boil, add 1 teaspoon of kosher salt to the pot, then simmer the potatoes until they are very soft, usually about 15 minutes. While the potatoes are cooking, caramelize the onions (see next step). Drain the potatoes, then transfer to a large bowl. Mashed the potatoes using a masher or a ricer. Set aside to come to room temperature.

Place the thinly sliced, half moon onions in a skillet along with the olive oil and remaining 1/2 teaspoon of salt. Cook over medium heat until the onions begin to brown slowly. Stir occasionally to make sure they don't burn. The onions should be dark golden brown, and very soft. This should take about 12 minutes. Add the caramelized onions to the mashed potatoes, and stir combine. Optional (recommended): Add a couple tablespoons of butter, olive oil, or unsweetened nut milk until the mixture is combines and the potatoes are creamy. IMPORTANT: taste the mixture for seasoning, and add a pinch more salt if necessary.

Preheat the oven to 400 degrees F. Remove the puff pastry from the fridge. Roll it out on a floured surface just slightly, creating a larger rectangle. Cut the pastry into 12 squares. Fill each square with a generous tablespoon of the mashed potato filling. Brush two of the four edges with the beaten egg. Fold the pastry in half, creating a triangle shaped pocket. Use a fork to crimp the edges closed. Brush each Boureka with beaten egg, then sprinkle generously with sesame seeds.

Bake for 20-25 minutes at 400 degrees F, until very golden brown and puffy.