In a small bowl, combine the warm milk, 1 teaspoon granulated sugar, and the active dry yeast. Let sit for 5 to 10 minutes until foamy.
In a large mixing bowl, whisk together the egg, egg yolk, vanilla extract, lemon zest, and 3 tablespoons of sugar. Add the yeast mixture and stir to combine.
Stir in the butter and salt. Slowly add the flour, one cup at a time, mixing until a soft dough forms. Knead for about 5 to 7 minutes until smooth and elastic.
Place the dough in a greased bowl, cover with a clean kitchen towel, and let it rise in a warm place for about 60 minutes or until doubled in size.
While the dough is rising, prepare the filling by stirring together lemon curd and 1 tablespoon lemon zest in a small bowl.
Once the dough has risen, punch it down and transfer to a lightly floured surface. Roll into a rectangle about 10 by 14 inches.
Spread the lemon filling down the center third of the dough lengthwise. With a sharp knife or kitchen scissors, cut slits on both long sides of the dough at a slight angle about one inch apart.
Starting at one end, fold the strips over the filling, crisscrossing them to form a braid. Tuck the ends underneath to seal.
Transfer the braid to a parchment-lined baking sheet. Cover lightly and let rise for 20 minutes while the oven preheats to 350°F (175°C).
Bake for 25 to 28 minutes or until golden brown. Remove from oven and let cool slightly.
In a small bowl, whisk together powdered sugar, lemon juice, and milk to make a glaze. Drizzle over the cooled braid before serving.