Thaw the Phyllo dough as per instructions - overnight in the refrigerator and an additional 3 to 4 hours at room temperature.
Preheat oven to 375° F.
Boil the potatoes until soft. Allow to cool. Peel and then crumble the potatoes.
Boil or microwave the edamame beans in some water until cooked soft.
Heat ½ tablespoon oil in a cooking pot. Add cumin seeds and when they start to splutter add the chopped onions and sauté. Make sure to add the onion before the cumin seeds start to turn too brown.
Then add the ginger garlic paste, garam masala, turmeric and stir few minutes. Add crumbled potatoes, boiled edamame, jalapeno, cilantro, lemon juice and salt as per taste and mix it all together.
Remove the phyllo dough sheets out of the package, unwrap and cover it with a damp thin kitchen towel. Mix the remaining oil with the whisked egg very well and set aside.
Unroll one phyllo sheet and lightly brush the oil-egg mixture over half the sheet and fold it over.
Place 2 to 2½ tablespoons of the potato edamame mixture along the center of the shorter side of the folded phyllo sheet leaving an inch on each side.
Fold over the edges of both the long sides of the phyllo dough over the filling and roll it up into a cigar shape making sure to brush a little bit of the oil-egg mixture or water to seal.
Place the prepared samosa pastry rolls on a parchment lined baking sheet leaving gaps between them.
Lightly brush the tops of the samosas with the oil-egg mixture and sprinkle the sesame seeds/black seeds or carom seeds. Traditionally carom seeds are used which impart the characteristic flavor to samosas.
Bake for about 15 to 20 minutes until nicely golden brown.
If the Crispy Potato Edamame Cigar Samosas do not turn golden brown enough, despite being baked well and crispy, you may broil the tops for a minute or so at the end. But be sure to be careful to not let them burn.
Nutrition facts not including added salt. Check for any additional salt in other ingredients and adjust.