Once the poolish is ready, turn on mixer to medium low speed fitted with the dough hook attachment.
Slowly spoon in Bread Flour, Sugar, the 15 grams of softened butter, remaining water, eggs, and sea salt. (Stir eggs gently with a fork prior to adding.)
Turn mixer up to medium speed and work the dough for 1-2 minutes.
Scrape bottom of bowl with a spatula to make sure all ingredients are incorporated.
Work dough again at medium speed for 2-3 minutes until a coarse but tacky dough is formed. If it is too dry add 1-2 Tbsp of water as needed.
Transfer dough to a lightly floured bowl, then dust lightly with All Purpose Flour. Cover bowl with plastic wrap and set in a warm draft free location to double in size 1-2 hrs.
Once dough has doubled in size, place on a lightly floured surface. Shape dough into in a oval, removing excess air, but without kneading the dough.
Wrap in plastic wrap again and place in the refrigerate over night.
** (Option to chill for only an hour and then laminate dough, chilling the laminated dough overnight before rolling out and baking the next day)