In a large mixing bowl or stand mixer, add eggs, vanilla extract, brown sugar, sugar, melted butter, lemon zest, and buttermilk. Whisk together until all ingredients are combined and smooth.

In a separate bowl, combine flour, baking powder, baking soda, nutmeg, and salt. Whisk together.

Using a silicone spatula or wooden spoon, fold dry ingredients into wet ingredients and mix until fully incorporated (about 30 seconds). Cover bowl with plastic wrap and cool in the refrigerator for 1 hour-1 1/2 hours.

Add flour to a work surface and roll out dough. Use a rolling pin to roll dough until about 1/2 inch thick. Use a circle cookie cutter to cut into donuts. Use a smaller circle cookie cutter (or the bottom of a piping tip, that's what I use) to cut the hole in the donut. Place donuts onto parchment paper and refrigerate for an additional 30 minutes.

Heat vegetable oil to 320 degrees F. Fry donuts 2-3 donuts at a time for 6-8 minutes, flipping donuts every two minutes. Remove donuts once golden brown and put on a cooling rack.

Allow donuts to cool for about 1-2 minutes. Mix together 3/4 cup sugar and 1 tbsp cinnamon. Dunk donuts into cinnamon sugar.