1.) In a microwave safe measuring cup, heat the milk and water for 30 seconds at a time until warmed throughout, about 2-3 times.
2.) In the bowl of a stand mixer add the envelope of active dry yeast and the sugar. Pour the warmed milk mixture on top and whisk lightly. Let it sit for 10 mins until frothy.
3.) Add the egg, and vanilla extract and whisk again. Next add in the flour and salt and mix on low- medium speed with the dough hook attached. Continue mixing until a soft dough forms.
4.) Cut the butter into cubes and with the mixer running on medium speed, add the butter to the mixture slowly, mixing in between each addition. Continue kneading the dough on medium speed for 3 minutes. The dough is ready when all of the butter is incorporated and the dough is slightly sticky.
5.) Pour the dough out onto a floured surface and knead for 30 seconds until no longer sticky. Place the dough back into the bowl, and leave it in a warm area (such as on top of your stove with the oven preheated) for 1 hour until double in size.
6.) Right before rolling out the dough, prepare the filling. In a small bowl combine the melted butter, brown sugar, cinnamon, and maple syrup and stir until combined. Set aside.
7.) Pour out the dough onto a lightly floured surface and roll into a 12×16 inch long rectangle. Spread the filling in the center of the dough, leaving 1 inch off of the sides.
8.) From the long side, roll the dough into a log and slice it into 1” slices. You can cut off the ends and discard them if they are too small or have no filling inside. Place the pieces with the cut side up in a 9×13” pan and leave them again to rest for 30 mins with a covered teal towel in a warm spot.
9.) Preheat the oven to 350°F and bake the buns for 20-25 mins until puffy and golden brown.
10.) While the buns are baking, maple the maple glaze. In a small bowl combine the confectioners sugar, maple syrup, and milk. Drizzle all over the buns when they come out of the oven and serve.