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1
Preheat the oven to 350 F.
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2
Place the sugar and lemon zest in a medium bowl and rub them together with your fingers until the sugar is slightly moist and fragrant, about 1- 2 minutes.
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3
In a large bowl, beat together the butter and Greek yogurt. Add the lemon zest sugar and the brown sugar and beat until fluffy. Beat in the eggs and vanilla.
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4
In a separate bowl whisk together the all purpose flour, whole wheat flour, baking soda, and salt. Add this to the wet mixture and beat until just combined.
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5
Using a wooden spoon, stir in the oats. Spoon the cookie dough onto an un-greased baking sheet about a tablespoon at a time, leaving at least an inch between each. I like to roll the dough into balls. Bake for 9-10 minutes.
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6
Remove pan from the oven and set it on a rack. Let the cookies cool on the pan for a few minutes before removing to a wire rack to cool completely.
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7
While the cookies cool, make the glaze. Put the juice from the Meyer lemons into a medium bowl. Whisk in the powdered sugar 1/2 cup at a time to reach the desired consistency. You can add more sugar if you like a thicker glaze.
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8
Lay a piece of wax paper down, spread the cooled cookies on top of it, and spoon the glaze over the cookies. Let the glaze set for a few minutes before serving.