In a large bowl mix together the water, milk, and yeast. Add the 3 cups of flour to the bowl and stir to combine. In a separate small bowl mix together the honey, butter, salt, and 1 egg then mix into the bowl with the flour mixture. Continue to mix until a dough is formed and pulls away from the sides of the bowl.
Lightly flour a work surface and knead the dough for about 5 minutes then form into a ball. Add the oil to a large clean bowl and add the dough ball, flipping the dough ball a couple times to coat in the oil. Loosely cover the bowl and allow the dough to rise in a warm place for 2 hours.
Transfer the dough to a lightly floured work surface and separate into 4 equal size pieces. Form each piece of dough into a dome shape by tucking the edges underneath and pinching the dough together on the bottom. Lightly flour a rimmed baking sheet and lay the domes on the baking sheet. Press down the domes so theyre roughly 4-inches in diameter (its ok if they look a little flat at this point, they will rise to more of a dome shape later). Generously sprinkle the buns with flour and allow to rise for 30 more minutes.
Preheat the oven to 375°F.
Beat the remaining egg in a small bowl then brush the tops of the buns. Sprinkle the poppy seeds on the top of the buns and bake in the preheated oven until golden brown on top, about 15 minutes.