In a small bowl, mix together the flour, baking soda, baking powder and set aside. In a large bowl cream the butter with the sugar. Add in the egg and vanilla, mix to combine. Add in the flour mixture little by little until incorporated. Add in just enough milk, adding in 1 Tablespoon at a time until the mix is moistened but not wet. Place cookie dough into fridge for at least one hour to set, if you skip this part your cookies will run on the pan when baking.
Preheat oven to 375 degrees. Using a Tablespoon scoop, roll out cookie balls, rolling them into the sugar and then placing them on a lined cookie sheet. Pat down each cookie so there is a flat surface on top. Bake 8-10 minutes, until the corners start to get golden brown. Place on wired rack for 5 minutes to cool then transfer cookies directly on to rack. Cool completely.
Key Lime Frosting
Place flour and milk in a small sauce pot over medium heat. Whisk to combine, continue to whisk until mixture comes to a bowl. When mixture thickens, take off the heat, add the vanilla, mix and let cool completely.
In a stand mixer (or hand mixer, but stand is easier), Place butter and sugar, mix until lightly and fluffy about 3 minutes on medium speed. Add in the milk mixture and beat on high until it forms the consistency of whipped cream this can take 5 to 10 minutes. Check mixture and if any sugar graininess is still there, whip some more. Add in the key lime juice until incorporated.
Cookie Assembly
Match up your cookies so they are roughly the same size. In the middle of each half, place about 2 teaspoons of raspberry curd. Place the frosting in a piping bag and pipe a swirl around the curd. Top with the other half of the cookie, serve and enjoy! Any cookies that are not eaten right away should be stored in the refrigerator in a sealed container.