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For the cookies:
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Preheat oven to 350 F and line 1 or 2 baking sheets with parchment paper or a Silpat mat.
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In a small saucepan over low heat, melt the butter. Remove from heat. Add the sugars, cocoa powder, and Kahlua to the butter and whisk it together. Add in the Greek yogurt and whisk until everything is combined. Set aside.
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In a medium sized bowl whisk together the flours, espresso powder, baking soda, and salt. Pour the chocolate mixture into the dry ingredients and fold together with a spatula until everything is incorporated.
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Use a cookie scoop to measure out the cookies. Roll each scoop into a ball, place on the baking sheet about 2 inches apart and then flatten each slightly with your hand (see note).
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Place them in the oven on the middle rack and bake for 8-10 minutes. Remove from oven. Let the cookies cool for a couple minutes on the baking sheet before removing them and putting them on a cooling rack.
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For the Bailey's buttercream:
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In the bowl of a stand mixer or in a mixing bowl using a handheld mixer add all of the ingredients. Beat the ingredients on medium to medium high speed until they all come together and become light and fluffy.
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To assemble the cookies:
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Once the cookies are cool, spread about a teaspoon or so of the buttercream on the bottom of one cookie. Place another cookie on top and press them together slightly. Repeat with the rest of the cookies and buttercream.
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Serve immediately or store in an airtight container.
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Notes: Be sure to flatten the dough balls slightly before putting them in the oven or they will be thick and puffy.
