Soften the cold butter - use a rolling pin, pound the butter to soften it. The butter should be pliable and soft. Set aside.

In an electric mixer with an attached dough hook, combine the flour, water, milk, eggs, yeast and salt. Mix at low speed until all ingredients are incorporated - about 2 to 3 minutes. Increase speed to medium and continue mixing the dough - about 5 to 8 minutes. The dough will start to become smoother.  

Note: The dough will look and feel dry. 

Add the sugar and incorporate at low speed - about 2 minutes. 

Add the softened butter and incorporate at low speed - 3 to 5 minutes.  Use a spatula to scrape down any butter that are caught on the sides of the bowl. 

Increase speed to medium and continue mixing until the butter is fully incorporated and the dough will feel wet and soft. 

Lightly oil a large mixing bowl. Remove the dough to the bowl (use a spatula to scrape out the dough if needed). Cover with plastic wrap and let it sit at room temperature for one and a half hours..

Fold the dough at the halfway mark (45 minutes) - to do this pull each corner of the dough into the middle.  Start the pull by placing your fingers underneath the middle of the dough. 

Divide the dough in two equal pieces (about 350 grams each). Preshape each piece of the dough into a round shape. Do this by folding each corner of the dough into the center. Flip the folded side down on the board and put the palm of your hand around the dough. Begin pulling the dough towards you until it’s tucked in. Quarter turn the dough and do the same process. Continue doing this for two more quarter turns until the dough is round. 

Place the dough on a board or sheet pan. Cover loosely with plastic wrap or a bread towel. Allow the dough to rest for 20 minutes. 

Complete the final shape - Batard (log). For this process place the dough seam side up and use your palm to “degas.”  That is, lightly flatten it until any bubbles are no longer visible. 

Now begin to shape into a log - fold the longer side of the dough towards the middle. Now fold the other longer side of the dough to the center.  Complete the log shape - place your thumb, starting at one end of the middle part of the dough and begin to fold it over to the edge and use the palm of your other hand to press and seal the seam.  

Please the dough, seam side down in a greased loaf pan.  Complete the final shape process with the remaining dough.  

Egg wash the dough on the top and sides (Use one egg, beaten). Cover the pans loosely with plastic wrap or a bread towel. Allow the dough to sit and proof for one and a half hours (The dough should have filled the pan and when gently touched should snap back to shape easily).

Preheat the oven to 350 degrees (convection setting if you have the feature).  Egg wash the dough again.  Place the loaf pans on a sheet pan.  Place the sheet pan with the dough in the oven and bake for 35 minutes until nice and medium brown.  Remove the Brioche from the oven and place the loaf pans on a cooling rack - cool for 10 minutes before removing from the pans.  Remove the bread from the pan and allow to cool completely on the cooling rack.

Note: To test for doneness you can use a thermometer to test the internal temperature - need to be 170 degree.  Or empty the dough and tap the bottom - will sound hollow. (these testing processes need to be done immediately after removing the bread from the oven).

Slice and enjoy!