Prepare Doughnut Dough: Combine warm water, yeast, and a pinch of the granulated sugar in a large mixing bowl. Allow to proof for 5 minutes in a warm place until foamy.
Add roughly 1 cup of the bread flour and mix well. Allow mixture dough to sit for 30 minutes, uncovered, in a warm space. Add the eggs, remaining sugar, salt, and melted butter and mix well. Add the remaining bread flour, stirring with a large wooden spoon or your hands until well incorporated.
Transfer the dough onto a well-floured countertop and knead until soft, smooth and well incorporated. The dough will be sticky, but avoid adding too much additional flour. Place the dough in a clean, lightly oiled bowl, cover tightly with plastic wrap, and allow to rest in a warm place until double in size, roughly 1 hour. Meanwhile, prepare the curd (see recipe below).
Once the dough has doubled in size, place on a lightly oiled countertop and press or roll the dough flat until it is roughly ¾-inch thick. Using a 3-inch biscuit cutter, cut the doughnuts and place each piece of dough on a small square of parchment paper. Cover the doughnuts with a kitchen towel and allow to rest for 15 minutes before frying.
Prepare Grapefruit Curd: Combine the grapefruit juice, sugar, cornstarch, egg yolks, whole eggs, and salt into a small saucepan. Whisk to combine. Place over medium-low heat and whisk continuously until the mixture thickens and comes to a slow boil. Boil for 2 minutes - this will cook the cornstarch through - before removing from heat. Whisk in the cold butter and vanilla extract.
Strain the curd through a fine-meshed sieve set over a large bowl. Use a spatula to press the curd through the sieve. Allow the curd to cool completely (if peparing in advance, cover and refrigerate, beating well before using).
Fry and Serve Doughnuts: Heat vegetable oil (roughly 8 cups) in a large Dutch oven until the temperatures reaches 350°F (175°C). Fry 2 to 3 donuts at a time, inverting the parchment paper and setting the doughnut into the oil until the parchment releases. Fry for 2 to 3 minutes on each side, flipping with a slotted spoon or skimmer, until golden brown on both sides. Transfer the fried doughnuts to a paper-towel lined sheet pan and allow to cool until just slightly warm to the touch.
Place a thin layer of granulated sugar on a small baking sheet or plate. Transfer the curd to a piping bag fitted with a round tip. Toss the cooled donuts in granulated sugar until well coated on each side. Use a pairing knife, puncture the side of each doughnut to form a small hole. Place the tip of the piping bag into the hole and pipe 1 to 2 teaspoons of grapefruit curd inside (roughly). Serve immediately.