In a bowl, dissolve the yeast in water part 1; allow to sit for 10 minutes, until foamy.
In a standing mixer with a dough hook attachment, add the butter, whole eggs part 1, sugar, salt, flour part 1, and yeast mixture. Mix at medium speed until smooth.
Add flour part 2 and continue mixing until the dough has developed, 6-7 minutes.
Shape the dough into a ball; cover the bowl and proof until doubled, 1 to 2 hours.
Punch down dough and reshape into a ball.
Cover and refrigerate 8 to 12 hours. Remove from the refrigerator, punch down dough and reshape into a ball.
In a small bowl, mix the whole eggs part 2 with the water. Cover and store in the refrigerator; this is the egg wash.
Coat 24 (1/2 cup each) muffin cups or brioche pans with nonstick cooking spray.
Turn dough out onto lightly floured surface; shape 24, 55 gram dough portions into balls and place in muffin/brioche cups
Portion remaining dough into 24, 10 gram pieces and roll each piece into a small ball.
Make ½-inch deep indentation in center of each larger dough ball. Place the smaller dough ball into each indentation.
Cover loosely with plastic wrap and proof for an additional 30 to 60 minutes in a warm, draft-free space.
Gently brush the egg wash onto tops of rolls.
Bake at 375° F until golden brown, 15 to 17 minutes.
Remove from pans; serve warm or cool completely.