Preheat oven to 350° F.
Add the melted butter (COOLED to keep sugar from dissolving), cane sugar, and brown sugar to a large bowl. Using a handheld mixer, mix on medium speed until the butter is well-incorporated into the sugar and there aren't any clumps of brown sugar left. The texture should be crumbly, not smooth.
⅔ cup unsalted butter, ⅔ cup cane sugar, 1 ¼ cup light brown sugar
Add the eggs and mix on medium speed until smooth. Add the pumpkin puree, Greek yogurt, and vanilla extract to the butter-sugar mix. Mix on medium speed until the ingredients are fully combined and the texture is smooth.
2 ¼ cup canned pure pumpkin puree*, 3 large eggs, ½ cup plain Greek yogurt**, 1 tablespoon vanilla extract
In a separate medium-sized bowl, whisk together the flour, baking powder, baking soda, salt, pumpkin spice, and cinnamon. Add the whisked dry ingredients to the bowl of wet ingredients, and stir with a rubber spatula until there aren't any pockets of flour left.
2 ½ cup all purpose flour, 2 teaspoon baking powder, 1 teaspoon baking soda, ¾ teaspoon fine sea salt, 2 ½ teaspoon pumpkin pie spice***, 1 ½ teaspoon ground cinnamon
Spoon the cake batter into the oiled bundt cake pan. Smooth the top with a rubber spatula.
Bake for about 40-50 minutes. Check it at 40 minutes--you'll know it's done if you can poke a toothpick into the thickest part of the cake and it comes out clean or with only a few crumbs. Leave the cake to cool in the pan for about 10 minutes.
Invert the cake over a cooling rack and gently lift off the pan. Then allow the cake to cool completely (at least an hour) before frosting.