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To make the dough: In a large bowl, combine the flour and salt with your fingers.
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Drizzle in the oil and mix with your fingers to incorporate the oil. Squeeze the dough occasionally to check for consistency; it should hold its shape but collapse when pressed.
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Add the water, 2 tablespoons at a time, working it in with your fingers. As you bring the dough together, occasionally press the top of the dough down with your knuckles.
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Once the dough is combined (this should take about 5 minutes total), shape it into a ball in the bowl, drizzle the top with oil, and drape a damp towel over the bowl. Let the dough rest for 30 minutes.
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To make the filling: While the dough is resting, heat a skillet or wok over medium-high heat. Add the oil, then the onion. Sauté until the onion is soft, 3 to 4 minutes.
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Add the ground chicken, breaking it up into little pieces. Season with 1 teaspoon of the salt, garlic/ginger paste, cumin, garam masala, black pepper, and nutmeg, stirring to combine. Cook until the chicken is cooked through, 5 to 7 minutes. Remove the pan from the heat and set aside.
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Whisk the eggs together in a medium bowl. Add the remaining 1/8 teaspoon salt, the cilantro, onion, and chilis (if using).
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Stir half the chicken mixture (about 1 1/4 cups, 175g) into the egg mixture; you can reserve the remaining chicken mixture for another use (omelet, taco, etc.) or freeze it to make paratha later.
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To assemble and fry the parathas: Heat 1 to 2 cups (198g to 396g) vegetable oil in a wok or deep skillet; you want the oil to be about 1” to 1 1/2” deep. Heat over low heat until the oil reaches 350°F.
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Divide the dough into 6 pieces; if you have a scale, each piece will weigh between 65g and 70g. Shape each piece into a square or rectangle.
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Lightly flour your work surface. Working with one piece of dough at a time, roll it into a 12" x 8" rectangle, flipping it occasionally to ensure it’s not sticking to the work surface. It should be very thin, to the point that it’s semi-translucent.
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Place 3 tablespoons of filling in the center of the dough and spread it into a thin, even layer, stopping about 2" away from the long edges and 3" away from the short edges.
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Bring the long edges of dough to the middle, then do the same with the short edges and press down to seal. You should have an approximately 6" x 4" paratha.
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Carefully lower the paratha into the hot oil, seam side down. Cook the paratha for 5 to 6 minutes, flipping it occasionally; be sure to monitor the temperature of your oil while the paratha is frying to ensure it doesn’t fluctuate too far above or below 350°F. Adjust by turning the heat up or down.
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Remove the paratha from the oil, allowing the oil to drain back into the wok or skillet, and place it on a paper towel-lined plate.
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Repeat the process with the remaining dough and filling. You can keep the parathas warm in a low oven (200°F to 250°F).
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Cut the parathas into quarters before serving.
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Store any leftovers, well wrapped, for several days in the refrigerator; freeze for longer storage. Rewarm in the oven before serving.
