Rinse the fresh cranberries thoroughly and place them in a saucepan with 1/2 cup of water and 6 tablespoons of granulated sugar. Bring the mixture to a boil over medium heat, then reduce to a simmer for 10-15 minutes, stirring occasionally, until the cranberries have broken down and resemble a chunky sauce. Allow the mixture to cool for at least 30 minutes.

Set your oven to 325°F (163°C) and ensure it's fully preheated by the time you start baking. Meanwhile, line a 9-inch square baking dish with parchment paper, leaving some overhang for easy removal later.

In a mixing bowl, combine 1/2 cup melted unsalted butter, 1 teaspoon vanilla extract, 1/4 cup granulated sugar, 1/4 teaspoon salt, and 1 cup plus 1 tablespoon all-purpose flour. Stir until the mixture becomes a soft dough. Press this dough evenly into the bottom of the prepared pan. Bake in the preheated oven for 16-18 minutes, or until the crust is lightly golden brown; set aside to cool for 20 minutes.

In another bowl, whisk together 3 tablespoons of flour, 1 cup of granulated sugar, 3 large eggs, and 1/2 cup of fresh lemon juice until smooth.

Spread the cooled cranberry mixture evenly over the cooled shortbread crust in the baking dish. Refrigerate this layer for about 45 minutes to allow it to set slightly before adding the lemon custard layer.

Increase the oven temperature to 350°F (177°C). Carefully pour the lemon layer mixture over the cold cranberry layer, ensuring an even distribution. Bake for 43-45 minutes or until the lemon layer is set and slightly firm to the touch; it should not jiggle in the middle. Once done, cool the bars on a wire rack.

After the bars have cooled at room temperature, refrigerate them for 1-2 hours to achieve the best texture before slicing. Once chilled, dust with powdered sugar for an elegant finish. Cut into squares and arrange on a serving platter.