Grease popover pan or muffin tin thoroughly with butter.
Heat milk and butter to lukewarm. When the butter just begins to melt is when it is warm enough.
Whisk together eggs, milk, pumpkin puree, and brown sugar until thoroughly combined. Stir flour and pumpkin pie spice. Batter will be runny.
Pour batter into popover pan or muffin tin filling ⅔ to ¾ full.
Place popovers in oven and bake for 20 minutes. Do not open the oven door during baking.
After 20 minutes, reduce heat to 350 (without opening oven door) and continue to bake another 10 to 15 minutes, until golden brown.
While popovers are baking, make your maple butter glaze. Combine maple syrup to melted warm butter and stir well to combine. Add confectioners sugar and mix until combined.
Remove popovers from oven and poke the top of each with the tip of a knife or fork tines to release steam.
Serve immediately with maple butter glaze or regular butter.