In a pan on the stove, or in the microwave, melt butter and set aside to cool.
In a large bowl, whisk the yogurt, milk, eggs, and vanilla. Sprinkle the flour evenly over the surface of the wet ingredients. Follow with the sugar, baking powder, baking soda, and kosher salt.
Using a silicone spatula, or wooden spoon, lightly mix the dry ingredients on top. Next fully mix the dry ingredients into the wet ingredients below. While there are still streaks of dry flour visible, add the cooled, melted butter and mix until just combined. Set aside to rest for 10 minutes.
Heat a nonstick pan, or griddle, over medium-low heat. Drop ⅓ to ½ cup of pancake batter onto the pan. It will spread out just a bit. After 2-3 minutes, bubbles will start to form on the edges and surface of the pancake.
When the edges look dry and and the bubbles begin to pop, use a thin pancake spatula to gently lift one side and peek underneath. When the pancake is golden brown, flip and cook on the other side for 2 to 3 minutes, or until the bottom of the pancake is golden brown and the pancake is fully cooked.
Place cooked pancakes in a pancake or tortilla warmer, or on a plate with a large bowl turned upside down over the top, to keep them warm.
Serve with butter, warm maple syrup, fresh fruit, or your favorite toppings.