Preheat your oven to 350°F. Line a 9 x 13" cake pan with parchment paper. Leave an overhang to make removing the bars from the pan easier.
Make the shortbread crust:
In a large bowl, whisk the flour, sugar, salt, egg yolks, and vanilla extract. Add the melted butter and stir with a wooden spoon until the dough is cohesive.
Spread the crust mixture evenly in the cake pan and use your fingers or the bottom of a measuring cup to press it down tightly and evenly into the pan.
Use a fork to poke several holes in the dough, then prebake the crust for 18 minutes. Start making the filling while the crust bakes.
Cranberry Lemon Filling:
Add the fresh or frozen cranberries to a large saucepan along with 1 cup of granulated sugar. Place the pan over medium heat, cook, and stir until the cranberries start to soften and release their liquid.
In a medium bowl, whisk the fresh-squeezed lemon juice, water, and cornstarch until the cornstarch is dissolved. Add it to the saucepan with the cranberries and bring the liquid to a boil. Use a wooden spoon or a potato masher to stir and break down the cranberries as they cook.
Take the pan off of the heat and set aside.
In a large bowl, whisk the eggs, egg yolks, remaining 1 and ½ cups granulated sugar, and the vanilla extract. Whisk vigorously until well combined.
Whisk the egg mixture into the saucepan with the warm cranberry lemon mixture. Whisk very well until combined and smooth.
Place the saucepan back over medium heat and bring the mixture to a boil, whisking occasionally.
Once boiling, lower the heat and continue to cook, whisking constantly, until bubbling and thick. About 3-5 minutes. Turn the heat to low and stir in the butter until melted.
Once the butter is melted, immediately strain the cranberry lemon mixture through a sieve and into a bowl. Use a spatula to press as much of the liquid through the sieve as you can.
Spread the cranberry lemon filling evenly over the prebaked shortbread crust. Bake the cranberry lemon bars for 10-12 minutes.
Remove from the oven and let cool completely at room temperature, then cover and refrigerate for at least 3 hours, but overnight is best.
When ready to serve, lift the cranberry lemon bars out of the pan and place on a cutting board. Use a large, sharp knife to slice into bars. Wipe the knife clean between each slice. Tip: For cleaner slices, place the pan in the freezer for about 30 minutes before cutting into bars.
Notes
CStore cranberry lemon bars in the fridge, covered, for 1 week. You can also freeze the bars, sliced or unsliced, and keep frozen for up to 3 months. Thaw overnight in the fridge before serving.