In the bowl of a stand mixer, combine yeast and warm water, let it sit for a few minutes. Add honey, oil, salt, and egg and mix to combine. Add 3 cups of flour and mix with the paddle attachment until the dough comes together in a sticky mass. Switch to a dough hook and turn mixer on low speed. Gradually add the remaining 1/2 to 1 cup of flour in. Continue kneading dough on low speed for about 8 minutes, until the dough is smooth and elastic.
Transfer dough to a lightly oiled bowl, turn once to coat, and cover with plastic wrap. Let rise in a warm, draft-free spot until doubled in size, approximately 2 hours.
Turn the dough out on to a lightly floured work surface and knead for 30 seconds. Cover with a clean towel and let rest for 10 minutes. Punch the dough down and divide into 12 equal sized pieces. Shape each piece into a smooth ball and place evenly into a lightly greased 9 or 10-inch pie dish. Cover with towel and let rise in a warm, draft-free spot for 20 to 30 minutes.
Pre-heat oven to 400 F. Mix the melted butter and honey together and brush the tops of the rolls. Bake for 15 to 20 minutes until the tops are golden brown. Cover loosely with foil and bake for an additional 10 minutes, or until the center of the rolls registers 190 F. Let cool slightly before serving.
To make the rolls a day ahead of time, prepare rolls up to the point of shaping. Do not allow another rise. Instead, cover with plastic wrap and place in the freezer for 2 to 4 hours. Then, transfer to the refrigerator and leave overnight to slowly rise. The following day, bake as directed but allow for additional baking time, approximately 2 to 3 minutes.