For the Dough: In a medium bowl, whisk together flour, yeast, baking soda, and salt. In a large bowl, using a stiff rubber spatula, vigorously stir butter and sugar together to form a uniform paste. Add flour mixture to butter mixture; wipe out bowl that had flour mixture, lightly grease with cooking spray or butter, and set aside. Using spatula followed by hands, mix flour and butter mixtures together until even, cornmeal-like mixture forms, 1 to 2 minutes.

Add yogurt and egg, and, using spatula followed by hands, stir until stiff, even dough forms, about 2 minutes. 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.

Place filling in center of dough and, using clean hands and rubber spatula, spread into an even 5-inch round disc, leaving a 3 1/2-inch border of dough on all sides. Starting at one edge, using your hands, fold and pleat dough over filling toward center, working your way around disc. Pinch and press pleats together to fully enclose filling. Press top of dough gently to form an even 6-inch round. Invert so seam side is facing down and, using a rolling pin, gently roll into an even 9-inch round. Carefully transfer to a rimmed baking sheet lined with parchment or a silicone baking mat.

Pinch dough around the edge of the gata between the index finger of one hand and thumb and index finger of the other hand to form decorative points, spaced about 1 inch apart. Brush top and sides of gata evenly with egg wash. Using a fork, drag flat underside of fork across top of gata to form grooved lines in a crisscross pattern, spaced about 1 inch apart. Using a toothpick, poke 8 to 10 evenly spaced holes in top of dough, stopping when you reach the filling. Bake until evenly golden brown, 28 to 35 minutes, rotating baking sheet after 20 minutes.