Place cubed potatoes in a large pot and cover with cold water (you want ~1-2" cold water above the potato cubes too).
Place pot over medium-high heat for ~25-30 minutes until potatoes are fully cooked and soft (a fork should go through easily).
Drain the cooked potatoes. Place the potatoes and minced garlic in a large mixing bowl and mash using your preferred method (I use my electric mixer but when doing so, be careful not to over-mix the potatoes).
Add the butter, salt and pumpkin pie spice and beat until butter is completely melted and spices are thoroughly mixed in with the potatoes. Then,slowly beat in the milk. Lastly, add the cheese, pumpkin puree and rosemary and stir/mix until cheese is completely melted and everything is combined.
Serve immediately. Store leftovers in an airtight container in the refrigerator for up to 5 days.