Transfer dough to the prepared lightly greased medium bowl and cover tightly. Let sit at room temperature for 30 minutes, then transfer to refrigerator and chill for at least 4 hours, and up to 16 hours.
For the Filling: In a medium bowl, stir together walnuts, flour, sugar, and salt. Add butter and vanilla extract and, using a rubber spatula, stir until clumpy paste forms and no dry flour remains, about 30 seconds. Cover and store at room temperature until ready to assemble.
To Finish and Bake: Adjust oven rack to middle position and preheat oven to 375°F (190°C). Transfer dough to clean, lightly-floured surface, and dust top of dough lightly with flour. Using hands, gently press dough into even 6-inch circle, adding flour to both sides of dough as needed to prevent sticking, while pinching closed any major cracks in dough that form. Using a rolling pin, roll dough into a 12-inch circle, about 1/4-inch thick.
