►DOUGH: Whisk together flour, sugar, and salt in a large chilled bowl. Add cubed butter and toss to coat. Use your fingers to cut butter into flour until mixture resembles coarse meal. If you find butter warming up at any point, refrigerate bowl for a few minutes.
►Whisk together eggs, water, and vinegar in a small bowl. Drizzle over flour-butter mixture. Using a rubber spatula, stir egg mixture into flour and mix until incorporated. You want dough to be hydrated, but not sticky—if it’s dry, add another tablespoon or two of water. Knead dough a few times, then divide into 2 even pieces. Form each piece into a disk, then wrap in plastic wrap and chill in the refrigerator for at least 1 hour, or preferably overnight.
►FILLING: Combine cream cheese, lemon zest, vanilla extract, and salt in a food processor and process until smooth. Cut guava paste into ¼-inch-thick slices (about 1 inch long and ¼ inch wide).
►TO ASSEMBLE: Roll out 1 dough disk on a lightly floured surface into a ¼-inch-thick round (12 to 13 inches across). Let dough relax for 5 minutes, then, using a cookie cutter or a cup, cut out 4-inch rounds. You should get 12 rounds; reroll dough scraps if needed. ►Transfer rounds to a parchment-lined rimmed baking sheet. Repeat with second disk.
►Place 4 pieces of guava paste on half of each round and top with 1 tablespoon cream cheese mixture. Brush dough edges with water, fold to create a half-moon, and seal by pressing dough together with your fingers. You can either crimp edges with a fork or try for traditional braided edge called repulgue: Starting at one corner, fold a triangle of dough down over itself. Press down to seal, extending that part a bit as you press on it. Fold down a second triangle right next to first. Press down to seal and repeat, working your way around edge. Tuck last triangle underneath itself, if necessary.
►Transfer pies to refrigerator and repeat process with second disk. Chill pies for at least 30 minutes or freeze for 20 minutes.
►Heat oven to 375°F. Lightly beat egg with milk in a small bowl. Brush empanadas with egg wash and sprinkle with coarse sugar. Bake until golden brown, 18 to 20 minutes. Cool for a few minutes, then dust with powdered sugar, if desired, and serve.