Whisk the yeast and warm water together in a large bowl. Allow to sit for 3 minutes until foamy. Add milk, egg, granulated sugar, and salt. Once these wet ingredients are mixed together, set the bowl aside and make your butter/flour mixture.
Cut butter into 1/4 inch slices and add to a food processor or blender. Top with flour. Pulse the mixture 10-12 times, until butter is fairly crumbled.
Pour the flour mixture into the wet ingredients. Very gently fold the two mixtures together. Do not be angry with the dough! You want to be very, very, very gentle when you are folding the two together. Fold *just until* the dry ingredients are moistened. The butter must remain in pieces, which creates a flaky pastry. Turn the dough out onto a large piece of plastic wrap. Wrap the dough up tightly and refrigerate for at least 4 hours or overnight.
After 4-12 hours, take the dough out of the refrigerator to begin the "rolling and folding" process. Flour a work surface. The dough will be sticky, so make sure you have flour nearby as you roll and fold. Using the palm of your hands, gently flatten the dough into a small square. From there, roll out into a 15 inch long rectangle using your rolling pin. You may have to continue to lightly flour the counter as you are rolling. Fold the dough together as if it were a business letter. And roll it out into a 15 inch long rectangle again. Then, fold again into a business letter. You'll repeat rolling and folding 1 more time for a total of 3 times.
Fold the dough up tightly, wrap in plastic wrap, and chill for at least 30 minutes or up to 1 day.
After at least 30 minutes, take the dough from the refrigerator and cut it in half. Wrap 1 half up and keep chilled as you work with the first half. Roll out your dough to make a 12x6 inch rectangle. I rolled this dough out onto a floured work surface, but I suggest you roll it out onto a lined baking sheet. (Lined with parchment paper or a silicone baking mat.) It is tough to transfer the braided dough from the counter to the baking sheet, unless you are very careful!
Cut off two corners of the dough and then two small triangles at the other end. (visual below)
Spread 1/2 of the filling (raspberry or cream cheese) down the length of the center of the strip. Cut slanting strips (3/4 inch - 1 inch each) along both sides. I used a very sharp knife, but a pastry wheel or pizza cutter will work just fine. I find this video VERY helpful. Fold the bottom end up to "seal" the filling in and allow the braid to rest for 15-20 minutes as you preheat your oven. Repeat with the second half of the dough and the rest of the filling.
Preheat oven to 400F. Beat the egg wash ingredients together. Brush the top of the pastry with egg wash. There will be enough egg wash for both braids. The egg wash gives your pastry that beautiful sheen.
Bake each braid for 15-16 minutes or until golden brown. Make sure to rotate the pan at least two times to ensure the braid is browning evenly. My oven has hot spots, so I rotated my braid every 5 minutes. Mine took 16 minutes.
Allow to cool for at least 10 minutes. Drizzle with glaze, slice, and enjoy!
*I tested this dough with 1% and skim milk. Would also work with 2% or whole. Avoid nondairy milk.
Make Ahead: prepare the dough through step 3. The dough at this point can be chilled overnight and up to 3 days. OR prepare the dough through step 5. Fold the dough up tightly, wrap in plastic wrap, and chill in the refrigerator for up to 1 day. During this second chilling time, you could actually keep the dough frozen for up to 1 month. Then thaw overnight in the refrigerator when you are ready to shape in step 6.