For sour cream pastry, process flour, butter and a pinch of salt in a food processor until fine crumbs form. Add sour cream, process until dough comes together then turn onto on a lightly floured surface and knead lightly. Form dough into a rectangular block, wrap in plastic wrap and refrigerate until chilled (1 hour).
Meanwhile, for caramelised onions, heat oil in a very large saucepan over low heat, add onions and stir occasionally, scraping base of pan if onion starts to stick, until very tender and caramelised (1-1¼ hours), adding garlic and thyme during the last 15 minutes of cooking. Stir through sugar and vinegar and cook until reduced (3-5 minutes), season to taste, set aside.
Roll out pastry on a lightly floured surface to a rough 24cm x 32cm rectangle. Transfer to an oven tray lined with baking paper then refrigerate to rest (30 minutes).
Preheat oven to 180C. Bake pastry until light golden and crisp (20-25 minutes), then place caramelised onion on top, scatter with anchovies and olives and bake until warmed through and golden (10-15 minutes). Scatter with chives, cut into portions and serve warm or at room temperature.