Combine dry ingredients for dough in large bowl. Add water and olive oil and mix until rough dough begins to form. Add more water as necessary. Knead on lightly floured surface until smooth and pliant. Allow to rest, covered about 30 minutes while preparing filling.
Heat olive oil over medium heat in large heavy skillet or saute pan. Add chile, ginger, onions and garlic. Saute until onion is translucent, about three minutes. Add spices and cook another minute until fragrant. Add potatoes and gently crush with back of spoon to desired lumpy consistency. Add peas and lime juice, cook another minute and season to taste with salt and pepper.
Place all chutney ingredients in bowl of food processor or blender. Pulse until finely pureed. Adjust seasoning.
Roll dough 1/8" thick. Cut out circles using 3" round cutter. Spoon 2 Tbsp filling into center of each round, folding in half to form a half-moon. Brush beaten egg on insides of each round and seal by crimping outside firmly with tines of a fork.
In a large heavy pot, preheat oil to 350°F. Drop samosas in a few at a time. Be careful not to overcrowd pan and drop temperature. Fry samosas, flipping once, until both sides are golden brown, about 2 minutes per side. Serve warm with cilantro chutney.