Shape dough into a ball and place in a lightly oiled bowl, cover and put aside unrefrigerated. Soak anchovies in milk and put aside.
In a 12-inch skillet, heat 2 tbsp olive oil over medium heat until it shimmers. Add sliced onions to the pan along with thyme and salt. Cook uncovered over low-low heat until golden brown, about 45 minutes. Stir often. Transfer caramelized onions to a bowl to cool.
Set oven rack to middle and preheat oven to 475° (245°C). On a lightly floured work surface, roll dough into a ½" thick rectangle, accuracy isn't important. Place flat dough on a lightly greased baking tray.
Leaving a one-inch border, spread onions over surface of the dough. Rinse soaked anchovies in water then make diamond design over onions. Place ½ olive in middle of anchovy diamond shapes.
Drizzle with remaining olive oil and bake until crust is golden brown, about 15 minutes. Lightly salt and serve right away.