Proof dough with only 1/2 of flour? I would like to ask if it's possible to proof dough using only 1/2 of the flour, then adding the rest of the flour with the rest of the ingredients. 

The basis for my question is this video, https://www.youtube.com/watch?v=Ij4snv_9ro4

After quite some time just admiring the above video, it didn't occur to me that no initial rise or proofing was done to the dough after mixing everything as seen in the video: skim milk, flour, yeasted risen very wet dough, and honey, and more water, which was obviously to provide more hydration.

After mixing, a sizeable portion must have been scooped out of the mixer and sent to the pastry sheeter. The next rise was done prior to baking.
'Proofing' in the context of breads actually has multiple meanings. Proofing 'the yeast' is also known as 'Fermenting' and is 


  To make sure active dry yeast (not quick-rise yeast) is alive and
  active, you may first want to proof it


Proofing 'the dough' on the other hand 


  refers to the final rise dough undergoes, which takes place after
  being shaped into a loaf, and before it is baked.


The second article continues to elaborate that 


  the words proof and fermentation are sometimes used interchangeably.


When making a single loaf of bread at home most recipes want you to add flour in stages up to the final amount. In 'large operations' the flour can be added, in part, to the yeast slurry and then to the larger mixer, as we see in the video. As Joe commented, in the video they are making a puff-pastry, so the analogy isn't perfect, but the principal remains the same.