In a medium pot over medium heat, melt the butter, stirring occasionally, until browned and fragrant, about 2-3 minutes. Transfer to a large bowl and whisk in the pumpkin puree, apple cider, eggs, maple syrup, and vanilla.
Add flour, baking powder, baking soda, cinnamon, ginger, nutmeg, and salt to the wet mixture. Stir gently until just combined. Let it rest for 10 minutes.
To make the maple butter, mix softened butter, maple syrup, and a pinch of sea salt until smooth.
Preheat your waffle iron and cook the batter until golden and crisp according to your waffle maker's instructions. Serve topped with maple butter and extra syrup.