Preheat the oven to 350 degrees.
Prepare your crust per the package directions. If you are using a frozen crust you will need the deep-dish style and you will need to allow it to thaw. Very lightly spray your pie dish with a non-stick cooking spray, unless it is already non-stick, before adding the rolled pie crust or your homemade pie crust. Don’t use too much spray or your crust will be soggy. Crimp the edges if desired. Set the crust aside.
Cut all of the donut holes or mini donuts in half and set those aside.
Melt the butter in a small saucepan on the stove or in the microwave in a large glass measuring cup (a medium glass bowl will do just as well). Add the brown sugar, cinnamon and nutmeg and whisk to combine. Then, slowly add the eggs while continuing to whisk so that the warm butter does not cook the eggs. Add in 2 teaspoons of vanilla and whisk again so that everything is well blended.
Arrange the donut pieces in the pie shell. I like to put the holes cut side down and stagger the different flavors for a nice colorful effect
Pour the butter mixture as evenly as possible over the donuts. If the filling comes too close to the top edge of your pie dish you may have to discard some.
Bake the pie for 30 minutes or until the filling is set but still bubbly. I added a pie shield halfway through the baking time to assure that the crust did not brown too much. You can also do this with strips of foil placed on the edge if you don’t have a pie shield. Remove the pie from the oven and allow to cool completely on the counter.
Once cooled, prepare the glaze. Combine the powdered sugar with 2 teaspoons of vanilla and 2 Tablespoons of milk using a small whisk. You want the glaze to be pourable but nice and thick. Adjust your liquid and/or powdered sugar measurements to achieve this consistency. Gently pour the glaze over the cooled pie in whatever pattern you wish. Try to cover most of the surface so that each bite has some glaze.
Cut the pie into slices to serve.