In a large bowl, or the bowl of a stand mixer, beat together the butter and sugar until fully creamed (3 minutes). Add the vanilla and egg and mix again to combine.
Fold in the flour and baking powder. Place in the refrigerator to firm up for 20 minutes.
If making the jam, add all ingredients to a small saucepan. Bring to the boil and keep stirring for about 5 minutes until thick and all the fruit has mashed down. Set aside to cool. Once cool enough, place in a container in the refrigerator.
Pre-heat the oven to 350℉/170℃. Line two large baking trays.
Remove the cookie dough from the refrigerator. On a lightly floured surface, roll to 1/4 thick. Slice into about 20 rectangles (I find it easiest to divide the dough into two balls and then cut 10 rectangles from each). A ruler helps if you want them to be more even!
Place the cookies onto the lined baking trays. They do not spread much so only need to be placed about an inch apart. Bake 12-15 minutes. Let cool on a wire rack.
Once cool, pair up the cookies. Spread one side of a cookie with a teaspoon or so of the strawberry jam and sandwich together with a similar sized cookie. Repeat for all.
Once all cookies are filled, make the glaze by combining the milk and powdered sugar. The glaze should be so thick it is spreadable but won't slip off the cookies. Spread over the top of each sandwich cookie and top with some rainbow sprinkles. Let set in the refrigerator before serving!