Cut out circles with a 2-inch round cookie cutter. Place the circles on the prepared baking sheet.
Bake the cookies for about 15-16 minutes until they are set and just beginning to brown. Transfer the cookies to a cooling rack and cool completely.
Make the filling:
Beat the butter together with the vanilla extract until it is creamy and smooth.
Add in the lemon zest and mix it in.
Beat in the confectioner's sugar 1 cup at a time: mix it into the butter thoroughly before adding in a splash of the lemon juice. Continue alternating the sugar and lemon juice, beating on medium speed until the frosting is fluffy and smooth.
Assemble the cookies:
Spread the bottom of one cookie with about 1½ teaspoons of the lemon frosting. Spread the bottom of another cookie with about ½ teaspoon of the jam.
Sandwich the two cookies together and place on a platter.
Continue with the rest of the cookies and fillings.
The sandwich cookies can be served at room temperature or chilled first in the refrigerator.
The cookies can be stored in a sealed container in the fridge for up to two days. Makes about 34 sandwich cookies