In a medium bowl, combine the yeast, warm water, and 1/2 teaspoon of sugar and give it a little stir. Let it sit for about 5 minutes, until it becomes foamy on top., Meanwhile, in a large bowl mix together the flour, salt, and remaining 2 tablespoons sugar. In a medium bowl, whisk together the eggs, oil, and additional sweetener., When the yeast is foamy, add it to the dry mixture immediately followed by the egg mixture and stir to combine. Knead until you have a smooth and slightly sticky dough, 7 to 10 minutes, adding more flour as necessary., Transfer the dough to an oiled bowl, cover it with plastic wrap, and let it sit at room temperature until doubled in size, 1 1/2 to 2 hours. Alternatively, you can refrigerate it overnight and then let it sit at room temperature for about 1 hour before shaping., Line a baking sheet with parchment paper. Pat the dough out into a long rectangle, roughly 3" x 12". Cut the dough into three long, skinny rectangles and roll them out a bit to get three long logs. Pinch them together at one end and then braid the logs, pinching them together at the other end. Transfer the loaf to the baking sheet and let it rise, covered, at room temperature for 30 minutes, until slightly puffy., Preheat the oven to 375°F. Brush the loaf lightly with the egg wash and sprinkle with sea salt. Bake until the loaf is golden brown and has an internal temperature of 190°F; begin checking for doneness at 28 minutes., Remove the loaf from the oven, and cool it on a rack before slicing. Store any leftovers at room temperature for several days; freeze for longer storage., Store any leftovers at room temperature, well wrapped, for several days. Freeze for longer storage.