In a large bowl, whisk together the flour, baking powder, baking soda, and salt until evenly combined. Set aside.
Melt the butter in the microwave and let it cool to slightly warm. Do not use it hot.
In a separate medium bowl, add the granulated sugar and brown sugar. Pour the slightly warm melted butter over the sugars and beat by hand for about 2 minutes, or use a stand mixer or hand mixer for about 1 minute, until well combined.
Microwave the Greek yogurt for 30 seconds and stir well to distribute the heat evenly. The yogurt should feel slightly warm, not hot. This step takes the chill off and helps the batter come together smoothly.
Add the warmed Greek yogurt to the butter and sugar mixture. Whisk by hand for 1 to 2 minutes, or mix in a stand mixer for about 1 minute, until fully combined with no streaks.
Add the eggs one at a time, whisking well after each addition.
Add the sourdough discard or active starter and vanilla extract. Whisk until smooth.
Pour the wet ingredients into the dry ingredients. Fold gently with a rubber spatula until just combined. Stop the moment you no longer see dry flour streaks. The batter will be thick. Do not overmix.
Fold in the chocolate chips, reserving a small handful to press onto the tops of the muffins before baking.