In a small bowl, combine warm milk and yeast. Let it sit for about 5 minutes, until frothy.
In a large mixing bowl, combine flour, sugar, and salt. Make a well in the center and add melted butter, eggs, vanilla extract, and the yeast mixture.
Mix until a soft dough forms. Knead on a floured surface for about 5-7 minutes until smooth and elastic.
Place the dough in a greased bowl, cover with a kitchen towel, and let it rise in a warm place for about 1 hour, or until doubled in size.
While the dough rises, prepare the filling by mixing softened butter, brown sugar, and cinnamon in a bowl until combined.
Preheat the oven to 350°F (175°C). Line a baking sheet with parchment paper.
Once the dough has risen, punch it down and roll it out on a floured surface to about ¼-inch thickness.
Spread the cinnamon filling evenly over the dough and cut it into strips.
Take a strip and form it into a bunny shape by rolling it into a ball for the body and two small pieces for the ears. Place them on the baking sheet.
In a small bowl, whisk the egg and brush it over the buns for a nice golden finish.
Add raisins or chocolate chips for the eyes, and sprinkle colored sprinkles on top if desired.
Bake in the preheated oven for about 20-25 minutes, or until golden brown.
Let the Bunny Buns cool on a wire rack before serving.