Heat Milk (1 1/4 cup) and Honey (1/3 cup) together in a small saucepan just until the honey melts and the milk becomes lukewarm. If the mixture overheats, wait until the milk cools down to lukewarm again.
Add the Active Dry Yeast (1 tablespoon), and gently stir together. Let rest for 10 minutes until the yeast has foamed. If it hasn't foamed, the yeast isn't active. Use new yeast, and start over.
In a standing mixer with a paddle attachment, mix the Butter (1/4 cup), Salt (1 teaspoon), and Egg (1) together. Add in the milk and yeast mixture until combined.
Add All-Purpose Flour (1 1/2 cup) and mix until the batter is smooth.
Remove the paddle attachment and attach the dough hook. Add the remaining All-Purpose Flour (2 1/2 cup) and knead for 3-5 minutes.
Place the dough in an oiled, medium to large bowl. Cover and place in a warm and dry place, and let rise for 1 hour.
Place some oil on your knuckles and punch down the dough. The dough will be sticky. Dump onto a floured surface and roll out until dough is about 1/4-inch thick.
Cut into rectangles, about 2x3 inches.
Place on cookie sheet, cover with a towel, and set aside to rest for 40 minutes.
Preheat the oven to 350 degrees F (180 degrees C).
Bake the rolls for 10-15 minutes. They are done once they just barely start to turn golden. You don't want to over bake. Immediately brush with additional melted butter.
Drizzle with additional honey if desired and serve warm.