Combine the flour, sour cream, butter, baking powder, and salt in a bowl or food processor. Mix just until a dough forms. Wrap and refrigerate for 30 minutes.
In a second bowl, mix the cottage cheese, grated cheese, feta, lemon zest, za’atar, and black pepper until evenly combined.
Roll the dough on a lightly floured surface to about ⅛ inch thick. Cut into 3-inch rounds, rerolling the scraps as needed.
Place a heaping tablespoon of filling in the center of each round. Fold into half-moons and seal the edges well. Arrange on a parchment-lined baking sheet, leaving space between each piece. Freeze at this stage, if desired.
Whisk the egg, water, and date syrup together. Brush over the bourekas and sprinkle with seeds.
Bake at 350°F/180°C, preferably on convection, until golden and crisp, 25 to 30 minutes. Some cheese may bubble out and caramelize at the edges. Serve warm.