Rinse and pick through cranberries, discarding any spoiled ones. In a medium saucepan, combine cranberries, water, and 6 tablespoons sugar. Bring to a boil over medium-high heat, then reduce to medium-low, cover with a splatter screen, and simmer while stirring occasionally for 10-15 minutes until cranberries have broken down. Set aside to cool for at least 30 minutes.

While crust cools, whisk together 1 cup granulated sugar and 3 tablespoons flour in a medium bowl. Add eggs and whisk until smooth. Stir in fresh lemon juice and set aside.

Preheat the oven to 325°F. Line a 9-inch square baking dish with parchment paper, ensuring edges are well covered for easy bar removal. Grease the parchment with butter or non-stick spray.

In a medium bowl, mix melted butter, vanilla extract, 1/4 cup granulated sugar, and salt until combined. Gradually mix in flour to form a thick dough. Press this dough firmly and evenly into the prepared pan, making sure it reaches all edges to prevent filling seepage.

Bake the crust for 16-18 minutes until lightly golden. Remove from oven and poke the crust all over with a fork to allow steam to escape. Turn off the oven. Let the crust cool for about 20 minutes.

Pour cooled cranberry filling evenly over the cooled crust, spreading it edge to edge. Refrigerate for 45 minutes to set.

Preheat oven to 350°F. Remove pan from refrigerator, carefully pour lemon layer over the cranberry layer, and bake for 43-45 minutes until the center is set and no longer jiggles.

Let the bars cool on a wire rack in the pan for 1 hour at room temperature, then refrigerate for 1-2 hours to fully set. Lift bars out using parchment overhang, sprinkle with powdered sugar if desired, and cut into 16 squares, wiping knife clean between cuts for neat slices.