Make your brown butter by adding the butter to a light-colored pan over medium-low heat. Let it melt, stirring occasionally. Do not walk away, as the process can move quickly once the butter melts. The butter will start to bubble and sizzle. After about 5-8 minutes, the milk solids will turn golden brown. Stir continuously once you see color forming. Remove from heat immediately and transfer to a separate bowl. Let it cool slightly in the refrigerator before adding it to the batter.
In a medium bowl, add the flour, salt, baking powder, and baking soda. Whisk together and set aside.
In a large mixing bowl, combine the eggs, honey, buttermilk, Greek yogurt, vanilla extract, and cooled brown butter. Mix until fully combined.
Add the flour mixture into the wet ingredients. Stir until just combined. The batter will be thick. Do not overmix.
Heat a small pat of butter or a drizzle of oil in a large skillet over medium heat. Add a ladle of batter and gently help it form a round shape if needed. Cook until the edges are set and the bottom is golden brown. Flip and cook the other side. Repeat with the remaining batter. You should get about 5 large pancakes or 8 smaller ones.
Serve immediately with your favorite toppings and enjoy!