In a large mixing bowl, combine the flour, sugar, salt, and baking powder. Whisk together until well combined and set aside.
Slowly add the warm water to the dry ingredients, stirring with a wooden spoon until a dough forms. You may need to add a little more water if the dough is too dry or a little more flour if it's too wet. The dough should be soft and pliable, but not sticky.
Turn the dough out onto a lightly floured surface and knead it for about 5 minutes, until it becomes smooth and elastic. Cover the dough with a damp cloth and let it rest for 10 minutes.
Divide the dough into small pieces, about the size of a ping pong ball. You can make them larger or smaller depending on your preference.
Roll each piece of dough into a ball, then use a rolling pin to flatten it into a thin disk, about 1/4 inch thick. You can also use your hands to stretch the dough if you prefer.
Heat the vegetable oil in a deep frying pan or Dutch oven over medium-high heat until it reaches 350°F. Carefully add a few domplines to the oil at a time, being careful not to overcrowd the pan. Fry for about 2-3 minutes on each side, until they are golden brown and crispy.