In a mixing bowl, add the flour, salt, room temperature butter, and water.
Using a bench mixer with a dough hook attachment, knead for 20 minutes until a smooth dough forms.
Remove the dough from the bowl, cover it well with plastic wrap, and let it rest for 30 minutes.
After resting, divide the dough into 4 balls, each weighing roughly 250g.
Generously coat each dough ball in room temperature butter, press them into small pancakes, and let them rest for another 20 minutes.
After resting, press each dough ball into discs about the size of a large pita bread (dinner plate).
Butter two of the discs and stack them, buttered sides together, on top of the other two discs. Cover with plastic wrap and let the dough rest again for 20 minutes. You should have 2 double-layered discs, one for each bougatsa.