Preheat the oven to 350 F and place a rack in the center.
Line the base of 2 8" cake pans with a parchment round. *See tips if you want to make a different size.
In a medium pot add in the butter and turn the heat onto medium low. We are browning the butter. First it will melt, then be loud and popping. Then it'll quiet down and foam - at this point you want to stir it and scrape the bottom of the pan - then it will foam again and this time brown bits should rise to the top. At this point your butter is brown but not before!
Remove the pot from the heat and pour the brown butter with all the bits into a heat safe measuring cup or bowl. Set aside on the counter.
In a medium mixing bowl, add in the eggs, sugar, vanilla, almond, and salt. Use an electric mixer to whip on high until fluffy. Then add in the greek yogurt and whip again until smooth.
With the mixer running on medium speed, slowly pour in the brown butter. It's ok if it's still a bit hot. You want the stream of brown butter to hit next to the beaters - try not to hit them or you'll spray hot butter everywhere.
Pour in the flour and then the baking soda and baking powder on top of the flour. Mix once more until mostly combined.
Use a flat rubber spatula scrape the bottom and edges of the bowl to ensure the dry and wet are completely combined.
Divide the cake batter evenly between the 2 pans. Smooth out the cake with a rubber or offset spatula.
Bake the cakes in the hot oven for 15 minutes. After 15 minutes, rotate the cakes and bake again for another 10-15 minutes until golden brown on the edges and set in the center.
Take the pans out of the oven and leave them to cool for 10 minutes. Flip the partially cooled cakes out and leave them to cool completely on a wire rack. *If you are prepping these a day before frosting, wrap them in plastic wrap and store in an air tight zip top bag at room temperature NOT the fridge.