In the bowl of a stand mixer, whisk the warm water and the 2 tablespoons sugar. Whisk in the yeast and let it get foamy, for 5-6.Whisk in remaining 1/2 cup sugar, 1/2 cup oil turmeric, and 3 of the eggs. Add the flour and fine sea salt, then fit the mixer with the dough hook and mix on medium speed until shaggy but unified, 3 minutes.
Continue to knead on medium speed until the dough is smooth and plush without being sticky and pulls away from the mixer without leaving any dough on the sides or bottom of the bowl, 7 to 8 minutes
Use a pastry brush to coat a large bowl with oil, add the dough, flip it to coat, seal with plastic wrap, then cover with a clean kitchen towel and let the dough sit in a warm place until at least doubled but ideally tripled in size, 1 hour 30 minutes to 2 hours for double and 3 hours.
Uncover the dough and punch it down with your fist, then transfer the dough from the bowl to the work surface.
Cut the dough into 2 equal-sized pieces then cut each larger piece into 3 smaller pieces.
Line a large baking sheet with parchment paper. Press down on each piece of dough to release any air bubbles, roll each into a 12-inch log then roll out and taper the ends of each log to form 16-inch logs. Let the logs rest for 5 minutes to allow the gluten to relax. Pinch the top ends together, pressing down the pinched top with a chef’s knife to secure the dough. Braid the logs, forming a challah that is slightly tapered on both ends and plump and generous as it reaches the center. Tuck the ends under and arrange the loaves on the parchment-lined sheet, leaving at least 4 inches between loaves. Let rise, covered, in a warm, draft-free place, until the challahs puff and nearly double in volume, 1 hour.
During the last 15 minutes of rising, set a rack in the center of the oven and preheat the oven to 350°F.
Beat the remaining egg in a small bowl, then brush the challahs thoroughly all over with the egg, Coat each challah with sprinkles, sprinkle with the flaky sea salt and bake until the challahs are golden and fluffy and the undersides are a lovely golden brown color and sound hollow when tapped, 32 to 34 minutes. Cool and slice.
