Carefully cut the butternut squash in half from stem to base. I like to lightly wedge my knife in the middle of the squash and then push down with both hands to sink the blade into the squash. Once the blade is fully into the squash, you can more forcefully push down spitting the squash in half. 

Use a spoon or metal ice cream scoop to scoop the seeds and any stringy parts out of the base of the squash. 

Line a baking sheet with aluminum foil and place the squash halves down skin side up. 

Bake at 400 degrees for 40-50 minutes or until the skin begins to pull away and the flesh of the squash is cooked through and easy to scoop out. 

Let the squash cool until you can work with it and begin scooping out the cooked flesh with a spoon or ice cream scoop. 

Store the cooked squash in an air tight container. If the squash is watery, drain the excess water in a colander. 

Begin by blooming the yeast in the warm milk in the bowl of a stand mixer. The milk should be the temperature of warm bathwater. If the milk is too hot it will kill the yeasts. 

In a small bowl melt butter in the microwave. Allow to cool slightly so it doesn't kill the yeast. 

Add the pureed butternut, melted butter, eggs and vanilla to the yeast milk mixture stir to combine. 

In a separate bowl combine the dry ingredients: all purpose flour, brown sugar, cinnamon, pumpkin pie spice, and salt. Mix thoroughly. 

Add the dry mixture to the wet mixture and stir together on low speed. The mixture will be a thick consistency. Once the ingredients are fully combined, knead the dough on low to medium for 5 minutes or until the dough begins to pull away from the sides of the bowl. Remove the dough from the bowl and oil the bowl. Return dough to the bowl and cover with plastic wrap. 

Let the dough rise in a warm spot for 1 hour or until doubled in size. 

Once dough has doubled in size, turn it out on a lightly floured surface and roll to 1/2 an inch thick using a rolling pin. Use a 3 inch donut cutter or biscuit cutter to cut out donuts. If using a biscuit cutter, you will have to use your thumbs to make a hole in the center of the donut. You won't have donut holes if you use this method. 

Arrange the cut donuts on a parchment lined baking tray and cover with plastic wrap. Let them rise in a warm spot for another 45 minutes to an hour. 

Heat 4 cups of lard (or oil of your choice) in a large pot or electric fryer. I used a Fry Daddy which is an electric deep fryer that regulates the temperature for you. The oil should be bubbling and immediately begin frying when flour is sprinkled into it. If you have an instant read thermometer make sure the oil is between 350 degrees and 380 degrees. 

Fry donuts for approximately 30 seconds per side. Donut holes fry much faster at approximately 15 seconds per side. Because they are tricky to flip, I set a timer for 30 seconds and just use my spider strainer to move them around periodically so all sides are cooked equally. The frying time will vary based on how hot your oil is and how thick your donuts are. Do a trial run of one or two donuts and cut them open to check the inside for doneness before frying the rest of the batch. Use a spider strainer to flip the donuts and remove them from the hot grease. Donuts should be golden brown on both sides when done. 

Place fried donuts on a wire rack on a baking sheet to drip dry. Line the baking sheet with parchment paper for easy clean up. Continue this process until all dough is fried. 

Mix together maple syrup, cinnamon and melted butter to make a glaze. 

Dip the donuts and donut holes while still warm on all sides and return to the wire rack to drip dry.