Brown butter. Add the 6 tbsp of butter to a saucepan over medium-high heat. Allow to melt and brown, while stirring continuously (~5-8 mins). Remove & pour into a large bowl. Place in the fridge to cool and harden up until smoothable.
Bring the apple cider to a boil in a small saucepan over high heat. Boil for 1 min, then reduce to medium heat. Allow it to gently boil, stirring occasionally, until the liquid is reduced a little more than half, leaving ¾ cup liquid (~15 mins). Set aside & cool completely.
Make the dough. In a medium bowl, whisk together the flour, baking soda, baking powder, salt, and spices. Set aside.
In the bowl with the brown butter, add the sugars, and beat for 1 min.
Add the eggs and beat. Then add the vanilla, greek yogurt mixture (or buttermilk), and cooled apple cider. Mix on low until combined.
Add the dry ingredients to the wet, and mix until flour is incorporated. Cover the bowl & refrigerate for 1 hr.
Turn the dough onto a floured surface; roll to ~½" thick. Using a donut cutter or cup, cut out ~2" discs. Then using a smaller round cutter or knife, cut out small holes in the centers. Re-roll the scraps to cut more donuts.
Heat the avocado oil in a large pot until it reaches ~360-375F.
Working in batches, drop a few donuts into the hot oil. Cook for 1-2 mins per side, until a deep golden.
Transfer to a paper towel-lined cooling rack. Cool for ~1 min, then roll in cinnamon sugar.
Serve the donuts warm with a scoop of vanilla ice cream and drizzle of salted caramel.
