In a large bowl, combine 2 cups of flour, sugar, salt, and yeast. Mix well. In a separate bowl, whisk together warm milk, melted butter, and the egg. Pour the wet ingredients into the dry ingredients and stir until a dough forms.
Gradually add the remaining flour, kneading the dough until it becomes smooth and elastic. Cover the bowl with a damp cloth and let the dough rise in a warm place for 1 hour, or until it has doubled in size.
Preheat the oven to 375°F (190°C). Line a baking sheet with parchment paper. Divide the dough into 12 equal portions and roll each portion into a rope.
Pinch a ball off the end to be reserved for the tail, Then twist the remaining rope to form a bunny shape with ears. Place the shaped bunnies on the prepared baking sheet.
Dip each bunny's tail in water and dip it in sesame seeds for a furry look. Place the sesame ball onto the twisted bunny bun. Bake in the preheated oven for 12-15 minutes or until the buns are golden brown. Allow the Bunny Buns to cool slightly before serving.