Combine the flour, instant yeast, and ½ teaspoon of salt in a large bowl. Add the lukewarm water and 2 tablespoons of olive oil. Mix until a rough dough forms, then knead for 8–10 minutes until smooth and elastic. Add a little flour if excessively sticky, but keep the dough soft.
Place the dough in a lightly oiled bowl and cover it with a clean kitchen towel or reusable cover. Leave it in a warm place for about 45–60 minutes, or until roughly doubled in size. Rising time varies with room temperature.
While the dough rises, heat 2 tablespoons of olive oil in a wide skillet over medium-low heat. Add the sliced onions and remaining salt. Cook for 30–40 minutes, stirring regularly, until the onions become very soft, sweet, and lightly golden. Lower the heat if they start browning too quickly.
Add the optional garlic, thyme, bay leaf, and a little black pepper to the onions. Cook for another 2–3 minutes. Remove the bay leaf and allow the onion mixture to cool slightly. The topping should be soft and flavorful, not watery.
Preheat the oven to 220°C (425°F). Line a baking tray with parchment paper. Gently deflate the risen dough and roll or stretch it into a rectangle approximately 9 × 13 inches. Transfer it to the tray and press it evenly into shape. If the dough springs back, let it rest for 5 minutes before continuing.
Spread the cooked onions evenly over the dough, leaving a small border around the edges. Arrange the anchovy fillets in a simple crisscross or diagonal pattern and place the black olives between them. Drizzle lightly with olive oil if desired.
Bake for 20–25 minutes, or until the crust is cooked through and golden around the edges. The onions should look slightly caramelized, and the anchovies and olives should be settled into the topping. If the base needs extra color, bake for a few additional minutes while watching carefully.
Remove the tart from the oven and let it rest for 5–10 minutes. Cut into squares or long slices with a sharp knife. Serve warm or at room temperature, accompanied by a green salad or other Mediterranean-inspired dishes.