Activate yeast: In the bowl of a stand mixer fitted with a dough hook, add the warm water, sugar, and yeast. Stir together and let it sit for 5 minutes until the yeast becomes slightly foamy.
Knead: Add the flour, eggs, and salt and mix on low speed for 1 minute until the dough comes together. Turn the mixer up to medium speed and knead for 6-8 minutes.
Knead in butter: With the mixer running, add the softened butter a few cubes at a time until combined into the dough. Continue kneading for 6-8 minutes until the dough cleanly pulls away from the sides of the bowl.
Oil the bowl: Push the dough to one side of the bowl and oil the sides of the bowl. Push it to the other side of the bowl and oil the other side of the bowl.
First rise: Cover and let the dough proof at room temperature for 1-2 hours or in the fridge overnight until doubled in size.
Prep: Cut parchment paper into twelve 4x4" squares and place them on a baking sheet. Set aside.
Punch down dough: Punch the air out of the dough and turn it out onto a lightly floured surface. Press out the dough to remove any large air bubbles.
Divide dough: Roll the dough into a log and cut it in half. Cut each of the logs into 6 equal pieces. Weigh each piece and redistribute the dough until they weigh about 60-70g each.
Roll dough: With your hand in a claw shape, roll each piece of dough with firm pressure against a lightly floured surface until it becomes a tight ball. Place the dough ball on a square of parchment paper. Repeat with the rest of the pieces.
Second rise: Let the dough proof for 1-2 hours at room temperature. Once risen and puffy, gently press each dough ball down to flatten slightly.
Heat oil: In a large pot, heat about 2" of oil on medium-high heat until it reaches about 180°C (356°F).
Fry donuts: Lower the donuts into the oil by the corners of the parchment paper but don't overcrowd the pot. Use tongs to remove the parchment paper after about 10 seconds. Fry the donuts for 2-3 minutes on each side until golden brown.
Roll in sugar: Remove the donuts from the oil with a slotted spoon and place them on a wire rack. Fill a shallow bowl with granulated sugar. While the donuts are still warm, roll them in sugar.
Fill donuts: Insert a knife into the side of each donut and twist it around to create an opening. Transfer the cooled mango curd to a piping bag fitted with a round piping tip. Insert the piping tip into each donut and squeeze until the donuts are filled.