Preheat oven to 350°F. Line a 9x13-inch baking pan with parchment paper, leaving overhang on two sides for easy removal.

Mix flour and powdered sugar in a large bowl. Add melted butter and stir until crumbly but holds together when pressed.

Press mixture evenly into prepared pan using your hands or the bottom of a measuring cup.

Bake for 15-20 minutes until edges just begin to turn golden. Keep oven on.

Combine cranberries, lemon zest, ¾ cup sugar, and water in a medium saucepan. Bring to a simmer over medium-high heat, then reduce to medium-low. Cook for 15 minutes, stirring frequently, until cranberries break down completely.

Remove from heat. Use an immersion blender to blend until smooth, or transfer to a blender (cool 5 minutes first for safety).

Stir in lemon juice, remaining ¼ cup sugar, and 4 tbsp butter until fully melted and combined.

In a small bowl, whisk together eggs and egg yolks. Slowly whisk in 6 tablespoons of hot cranberry mixture, one tablespoon at a time, to prevent scrambling.

Whisk tempered egg mixture back into the cranberry mixture. Add ¼ cup flour and whisk until smooth.

Pour mixture through a fine-mesh sieve (optional) to remove cranberry skins and seeds.

Pour filling over baked crust and spread evenly.

Bake for 20-25 minutes until center is set and no longer jiggly.

Cool at room temperature for 1 hour, then refrigerate at least 2 hours (or overnight).

Use parchment overhang to lift bars from pan. Dust with powdered sugar if desired. Cut with a sharp knife dipped in hot water, wiping between cuts.