Preheat your oven and a pizza stone to 500°F (or up to 550°F if your oven can go higher.)
While the oven preheats, gently heat the olive oil in a heavy-bottomed skillet. Add the onions, thyme, bay leaf, garlic, salt and pepper, stirring to evenly coat with oil, and cook gently over medium low to low heat (lowering if necessary to prevent over-browning) for about 20 minutes, until the onions are softened and just lightly browning around the edges. Do not caramelize the onions completely or they will scorch in the oven giving a burned taste to the final product. Remove the bay leaf from the caramelized onions.
Dust your work surface with flour and gently stretch your pizza dough into a circle. Use a floured rolling pin to stretch the dough out until it is about 1/8-inch thick. Generously cover a pizza peel with semolina or cornmeal.
Spread the onion mixture (including the oil) to within 1/4-inch of the edges of the crust. Arrange the anchovies and olive halves over the top of the onions. Give the peel a gentle shake to be sure the dough isn't sticking. If it is, carefully lift that area and sprinkle more semolina or cornmeal underneath to fix it.
Slide the dressed dough onto the hot stone and bake for between 8 and 15 minutes, depending on the heat of your oven, or until it is evenly browned and crisp underneath. Use the peel to transfer the Pissaladière to a cutting board.
Cool for five minutes, cut into wedges and serve warm or at room temperature.