In the bowl of a stand mixer, mix together ½ cup (120 grams) warm water, 1 tablespoon (12 grams) sugar, and the yeast by hand; let sit until frothy, about 10 minutes.
Add 2 cups (250 grams) all-purpose flour, whole milk, melted butter, bread flour, coconut milk, eggs, salt, extracts, and remaining 3 tablespoons (36 grams) sugar to yeast mixture; Using the paddle attachment, beat on low speed until smooth. Increase mixer speed to medium; beat until well combined, about 1 minute. Add 2 cups (250 grams) all-purpose flour; beat on low speed until combined. Increase mixer speed to medium; beat until well combined, about 1 minute.
Switch to the dough hook attachment. Beat on medium speed until the dough begins to pull away from the sides of the bowl, 3 to 4 minutes; add up to remaining ¼ cup (31 grams) all-purpose flour, 1 tablespoon (8 grams) at a time, if necessary. (The dough will still be quite soft and slightly sticky but should not feel overly wet.)
Spray a large bowl with cooking spray. Place dough in bowl, turning to grease top. Cover and let rise in a warm, draft-free place (24°C/75°F) until doubled in size, 40 minutes to 1 hour. (Alternatively, cover and refrigerate overnight. When ready to use, proceed as directed.)
Place 3 large baking sheets upside down and spray with cooking spray. Cut 14 (6-inch) squares of parchment paper and place on prepared baking sheets. Spray parchment with cooking spray. Spray 3 large sheets of plastic wrap with cooking spray.
Punch the dough. Lightly dust a work surface with all-purpose flour; Turn the dough out onto a prepared surface and divide it into 14 portions (about 80 grams each). Roll 1 portion of dough into an 18-inch long log of equal thickness. (Keep the remaining dough covered with plastic wrap, sprayed side down.) Place a finger in the center of the dough log and fold the log in half crosswise. Twist the dough 4 to 5 times to resemble a rope and pinch the ends together. Repeat the operation with the remaining dough.
Gently transfer donuts to prepared parchment squares, spacing them 2 to 3 inches apart. Cover donuts with plastic wrap, sprinkled side down, and let rise in a warm, draft-free place (24°C/75°F) until puffy, 40 minutes to 1 hour.
In a large heavy-bottomed pot, pour the oil to a depth of 2 inches and heat over medium heat until a deep-fry thermometer registers 185°C (365°F).
Line 2 large rimmed baking sheets with paper towels.
Working in batches, use the parchment paper to gently scoop the donuts and add them to the oil. (Do not place the parchment paper in the oil.) Fry until golden brown, about 1 minute per side. Remove donuts from oil using a spider strainer and place on prepared pans. Leave to cool completely.
Line 2 large rimmed baking sheets with parchment paper; place racks on top.
Dip cooled donut halves into coconut-orange glaze; lift upwards and gently rotate in a circular motion to let excess drip off. Place donuts, glaze side up on prepared rack and let rest until glaze is set, 20 to 30 minutes. It is best to serve it the same day it was prepared.
