In a small bowl, combine the warm water, 2 teaspoons sugar, instant yeast and ½ cup flour, stirring well to combine. Loosely cover with plastic wrap and set aside for 10-15 minutes (to let the yeast "proof" -- it'll bubble up and look foamy.
In the bowl of your stand mixer combine the yeast mixture, yogurt, butter, eggs, sugar, salt, and vanilla. Add 4½ cups of flour and mix with the paddle attachment until the dough is a rough, shaggy mass. Switch to the dough hook and knead on speed 2 until a soft, smooth dough forms, about 5 to 6 minutes, adding more flour if needed to achieve the correct consistency. (Note: you can do this by hand if you don't have a stand mixer.)
Place the kneaded dough in a lightly greased bowl, cover with plastic wrap, and allow to rise for 60 to 90 minutes, until puffy and nearly doubled.
While the dough is rising, prepare the cream cheese filling. Combine the cream cheese, ¼ cup sugar, ¼ cup sour cream, 2 teaspoons fresh lemon juice and ¼ cup flour in a small bowl, mixing until smooth and lump-free. Set aside.
Make the lemon curd: using a vegetable peeler, remove the zest of the 3 lemons, being careful to avoid the white pith. Put the zest in a food processor fitted with the steel blade. Add the 1½ cups sugar and pulse until the zest is very finely minced into the sugar. Cream the ¼ pound of butter and beat in the sugar and lemon mixture. Add 4 eggs, 1 at a time, and then add the ½ cup fresh lemon juice and salt. Mix until combined. Pour the mixture into a 2 quart saucepan and cook over low heat until thickened (about 10 minutes), stirring constantly. The lemon curd will thicken at about 170 degrees F, or just below simmer. Remove from the heat and cool.
When the dough has risen sufficiently (to double in size), gently deflate it by punching it down just a bit and divide it in half. Cover half with plastic wrap and set it aside as you roll out the first piece into a 10" x 15" rectangle. Rolling on parchment paper makes moving the bread to the baking sheet much, much easier. Lightly press two lines down the dough lengthwise, to divide it into 3 equal sections. Spread half the cream cheese filling down the center section, and top with a ¼ to ½ cup of the lemon curd, leaving 1" free on all sides of the filling.
To form the "twist", cut 1" crosswise strips down the length of the outside sections, making sure you have the same number of strips down each side. Beginning on the left, lift the top dough strip and gently bring it across the filling diagonally. Repeat on the other side with the top dough strip, so that the two strips crisscross each other. Continue down the entire bread, alternating strips to form the loaf. Be sure to press the "twist" pieces together at the ends to keep a tight "seal" (note: King Arthur's recipe basically shows you how to do this to make a "braid" which is much prettier but harder to accomplish).
Repeat the rolling, filling, and "twist" steps for the second piece of dough, using the remaining cream cheese filling and lemon curd. Set both loaves aside, lightly covered, to rise for 45 to 50 minutes, or until quite puffy
Preheat the oven to 375°F. Brush the loaves with egg wash and sprinkle with coarse sparkling sugar, if desired. Bake for 25 to 30 minutes, or until the loaves are golden brown. Remove from the oven and cool for 15 to 20 minutes before serving.