In a large bowl, whisk together the eggs, ½ cup (120 ml) of the oil, yogurt, granulated sugar, and baking powder. Using a wooden spoon, gradually stir in 1½ cups (210 g) of the flour. Use your hands to knead the mixture for a few minutes into a smooth dough. If your mixture does not come together and feels a little loose, add more flour, 1 Tbsp at a time, and continue kneading it with your hands. When the dough is smooth, soft, and not sticky, loosely cover the bowl with a kitchen towel and let rest at room temperature for 2 hours.
On a lightly floured surface, use a rolling pin to roll out the dough into a large round that is about ½ in (13 mm) thick. Invert a small cup on the outer perimeter of the dough, placing only half of the cup on the dough before pressing down to cut the dough and create crescent-like shapes (not rounds). Arrange the crescent-shaped pieces on a tray and continue the process, rerolling the dough scraps as needed, until you’ve used all the dough.
Fill a medium Dutch oven with enough of the remaining 1 cup (240 ml) of oil to come about 1 in (2.5 cm) up the sides. Line a tray with paper towels. Warm the oil over medium heat for about 3 minutes, or until a small piece of dough dropped in bubbles up and turns golden.
Working in batches, fry the dough crescents, flipping once, for about 2 minutes per side, or until light brown all over. Use a slotted spoon to transfer the noon masti to the paper towel–lined tray and let cool to room temperature.
In a large bowl, whisk together the confectioners’ sugar and cardamom.
In batches, toss the cooled noon masti in the cardamom sugar until evenly coated. Serve warm or on room temperature on a platter, refreshing with cardamom sugar if needed. Noon masti will keep in the refrigerator for up to 1 week or in the freezer for up to 1 month.