In mixing bowl, beat butter, sugar, sour cream, egg and baking soda at medium speed until well combined.
Mix in ginger and vanilla.
Gradually beat in flour.
Cover and chill at least 1 hour, or overnight for best results.
Preheat oven to 375°F. In batches, roll chunks of dough to about 1/8-inch thickness (use well-floured surface and floured rolling pin).
Cut dough using 3-inch round cookie cutters.
Bake cookies 8 minutes or until they just begin to brown around the edges.
Carefully transfer to cooling rack and let cool completely before frosting.
Place cream cheese and butter in mixing bowl and mix on medium-high speed until light and fluffy.
Reduce mixer to low; gradually mix in powdered sugar, scraping sides of bowl occasionally.
Add vanilla; beat until well combined.
Heat large pot of water to boiling.
Fill large bowl with ice and water.
In batches, add lemon slices to boiling water and cook 1 minute.
Transfer lemon slices to ice water and let cool 2 minutes; drain.
Place 2 large skillets over medium heat.
Add 2 cups sugar and 2 cups water to each skillet; heat until sugar is dissolved, stirring occasionally.
Reduce heat to medium-low; divide lemon slices between skillets.
Simmer 1 hour or until rinds are translucent, stirring and turning lemons occasionally.
Check every 10 minutes to be sure sugar solution isn’t browning (reduce heat if necessary).
Transfer lemon slices to wire rack set over rimmed baking pan; cool completely.
Spread each cookie with about 1 tablespoon frosting and top with 1 candied lemon slice.