Line a 9 x 9 baking pan with parchment paper and set aside.
In a large bowl cream together the butter and sugar.
Add in the eggs and vanilla and mix well.
Mix in the flour, baking soda, and salt. Mix until a dough forms.
Press half of the dough into the bottom of the baking dish. Place in the freezer for 20 minutes.
Preheat the oven to 375 degrees.
Remove the baking dish from the freezer. Carefully lift out the frozen dough using the parchment paper.
Place another piece of parchment in the bottom of the baking dish and press the remaining dough into the bottom.
Spread the strawberry jam on top of the cookie crust.
Place the frozen dough on top of the strawberry jam and peel off the parchment layer.
Bake for 25-28 minutes or until the cookie is firm.
Remove from oven and cool completely.
To make the icing whisk together the powdered sugar, vanilla, and milk. Spread over top of the cookie bars and sprinkle with the rainbow sprinkles.
Allow the icing 30 minutes to harden then use the parchment to remove the bars from the pan. Cut into 16 squares and enjoy.