1. Beat the butter at medium speed with an electric mixer until smooth and pale yellow. Slowly add in the powdered sugar, beating until incorporated, then mix in the vanilla bean. Gradually add in the flour and salt, beating at low speed until blended. Mix in the lemon zest and turn dough out onto a sheet of plastic wrap.
2. Shape the shortbread dough into a log, no more than 2" in diameter. Wrap the log up in the plastic wrap and freeze for at least an hour (or up to 1 month).
3. Preheat oven to 350° and line a baking sheet with parchment paper. Place log onto a cutting board or large plate. Lightly brush dough with milk and sprinkle with demerara sugar, rotating the log as you work until all the dough is covered in sugar. Cut the log into 1/4" thick slices. Place slices 1 inch apart on the baking sheet and bake for 10-12 minutes or until edges are golden.
4. Remove shortbread from baking sheets and let cool completely before filling with jam.
5. Sandwich a teaspoon of jam in between 2 cookies. Cookies will keep in an airtight container for about a week.
Don't put too much jam on the cookie, or it will squeeze out the sides.