Preheat oven to 350. In a large bowl, beat butter with an electric mixer for about 30 seconds and then add the sugar, 1 Tbsp of lemon zest, baking soda, and cream of tartar. Mix until combined. Add in the egg and vanilla and mix again. Add the flour and mix until well combined. The dough should be a little crumbly.
Line two 8X8 pans with foil and press half of the dough into each pan. Bake for 12 minutes. Using the foil, lift the cookies from the pan and cool on a wire rack.
Once cookies are cooled, soften the ice cream and place in a large bowl. Add in the lemon curd and the remaining lemon zest.
Line one of the 9X9 pans with plastic wrap (I used wax paper, but I think plastic wrap would work better) and place one of the cookie squares in the pan. Spread the ice cream mixture on top and then top with the remaining cookie square.
Cover the pan and freeze overnight. For easier serving, cut the frozen bars into squares and wrap each square in plastic wrap, freezing each one individually until ready to eat.