In your stand mixer, combine bread flour, instant yeast, salt and sugar. Mix until combined.
In a small bowl, whisk the eggs and add in the honey. Whisk the honey into the eggs until combined.
Measure your water and make sure it is at the proper temperature (110 degrees).
Add egg and honey mixture, water and softened butter to the stand mixer. Turn the mixer on and mix using the dough hook. If your dough is too wet, add flour as necessary. When your dough starts to firm but is still a little sticky, remove from the mixer.
Place the dough in a large mixing bowl coated with olive oil. Allow the dough to rest until it doubles in size. This should take 45 minutes to an hour.
Grease your casserole dish or line it with parchment paper.
Once the dough has doubled in size, punch down the center of the dough with your fist and then remove the dough from the bowl onto your counter that has been coated in flour. Cut your dough in half and roll out one half of your dough until it is about ½ inch thick. You want to try and roll your dough into the shape of a rectangle the best you can.
In a small bowl, mix the rest of the softened butter with honey. Using a rubber spatula, spread half of the honey butter on the surface of the dough. Starting at the end closest to you, roll up the dough with the butter on the inside until you get a long roll. Cut the roll into 8 equal sections. Complete these steps for the other half of the dough.
Place the rolled buns in your casserole dish. Preheat your oven to 375 degrees. Let the rolls rest in a warm environment another 20-30 minutes so they can rise one more time.
Make an egg wash with eggs and water. Using a basting brush, brush the tops of the rolls with the egg wash. Place the rolls in the oven uncovered. Bake for 35-40 minutes. Serve warm with honey butter brushed on top and sea salt flakes spread on top of each roll.