Add the granulated sugar and brown sugar to the creamed butter. Blend on medium-low speed until just combined, scraping down the sides of the bowl as needed to ensure everything is incorporated.
Pause the mixer, then add the vanilla extract and eggs. Turn the mixer to medium speed, then increase to medium-high and beat until the mixture is lightly fluffy, about 1 minute. Turn the mixer to low and mix in the Greek yogurt. Pause the mixer again.
In a separate medium bowl, whisk together the flour, baking soda, and salt. With the mixer on low, gradually add the flour mixture to the wet ingredients. Increase the speed to medium and blend until just combined, scraping down the sides of the bowl. Return the mixer to low and gradually add the old-fashioned oats, blending on medium speed until thoroughly combined.
Reserve 1 cup of the chocolate chips and stir the remaining chocolate chips into the dough until evenly distributed. Using a tablespoon scoop, drop spoonfuls of dough onto the prepared baking sheets, leaving some space between them. Gently press a few of the reserved chocolate chips onto the top of each dough ball for a bakery-style finish.