Preheat oven to 375ºF/190ºC with the oven racks in the middle of the oven.
In a large bowl with a stand mixer with a paddle attachment, or using a hand mixer, beat butter and sugar on medium speed until light and fluffy, about 5 minutes, making sure to scrape down the sides of bowl.
Add egg, sour cream, vanilla, lemon zest, and juice and beat just until smooth.
In a separate medium bowl, combine cake flour, salt, baking powder, and baking soda. Stir flour mixture into wet ingredients with a large spoon, a little at a time until combined. Dough should be thick and sticky.
Line 2 baking sheets with parchment paper, and scoop large (2 heaping tablespoons) spoonfuls 1 inch (2.5 cm) apart onto the sheet. Swirl to flatten slightly into 3-inch (7.5 cm) circles as these will not spread too much. Try to make them as round as possible by molding with your fingers. You can also place the dough in a 3-inch (7.5 cm) round cookie cutter to shape perfectly, though you’ll have to smooth the edges even so. These are big, but not as big as NYC-sized cookies!
Bake for 12 minutes until the edges start to brown, rotating after 6 minutes. Cool for 5 minutes on the baking sheet and then finish cooling on cooling racks (at least 30 minutes).
Now it’s frosting time! In a small saucepan, place raspberries, water, and corn syrup and bring to a boil. Lower to a simmer and simmer for 10 minutes, stirring occasionally. Place powdered sugar in a large bowl heat proof and set aside.
Strain the raspberry mixture to remove the seeds (you should have about 1/3 cup (80 ml) after it’s strained) and add the mixture to the powdered sugar. Frosting should be thick but spreadable. If your frosting is very runny, add more powdered sugar. If it’s very thick, add a little hot water.
Melt chocolate over a double boiler or in the microwave (heat for 15 seconds at a time until melted, stirring each time), and then place in a separate medium bowl and let cool. Mix in a little less than half of the raspberry frosting mixture to make the chocolate frosting. Add a little hot water if the frosting is too thick and powdered sugar if it is too runny. It should be thick but spreadable. If the frosting stiffens up, a little hot water will help it smooth out too.
Frost each half of the flat side (the bottom) of cookies with pink frosting and then follow with the chocolate. Let the cookies dry on wax paper. Let harden before serving.