Using a large bowl of your stand mixer, mix together dry yeast, salt and 3/4 cup flour. In a microwave safe bowl heat milk, sugar and butter to very warm (120°F to 130°F). Add warm milk mixture to the dry ingredients and mix until moistened. Add the egg, lemon zest, vanilla and continue mixing until smooth. Add in 2 cups flour and mix until a soft dough form. If needed, add the remaining 1/4 cup flour. The dough should not be sticky.
Using a dough hook, mix the dough for 6 minutes on medium-low speed. Alternately, you can knead the dough by hand for 6 to 8 minutes until smooth and elastic. Cover the dough with a clean dish towel and allow it to rest for 10 minutes.
In a clean medium sized bowl, mix together the cream cheese, lemon juice and powder sugar until creamy and smooth. Set aside.
On a lightly floured surface roll dough out until it's approximately 17x10 inches. Transfer the dough to a large baking sheet lined with parchment paper. Spread the cream cheese mixture down the middle of the dough, long-wise, creating a strip that's approximately 4-inches in diameter. Using a knife, or kitchen shears, cut the dough into 1-inch strips on each side of the dough, just to the edge of the filling. Alternate cut strips from side to side, starting at the top, folding the strips in a overlapping braid pattern.
Cover and let rise in a warm, draft-free place 45 to 60 minutes or until doubled in size. Preheat oven to 375°F. Bake for 15-20 minutes, or until golden brown. Remove from the oven and allow to cool.
Instructions for Glaze:
In a medium bowl whisk together powdered sugar, lemon juice and 1 tablespoon of milk until smooth. Drizzle on top of the crisscross. Serve warm or at room temperature.