Put the flour, sugar and yeast in a large bowl or the bowl of a stand mixer. Mix (with the dough hook if you're using a mixer) and gradually add the lukewarm water* and olive oil until it comes together into a dough.
Add the salt** and the olive oil, then knead for 3 to 4 minutes, until smooth.
Return the dough to the bowl, cover with a clean kitchen towel, and let it rest for 1½ to 2 hours. It should double in size.
Thinly slice the onions and add them to a large skillet with a good drizzle of olive oil. Season with salt and cook over medium-low heat for about 45 minutes, stirring now and then, until deeply caramelized.
Stir in the balsamic vinegar (optional) and mix well.
Preheat the oven to 410°F (210°C) on convection, or 425°F (220°C) conventional.
On a lightly floured surface, roll the dough into a circle about 11 to 12 inches (28–30 cm). Pinch the edges to form a rim.
Spread the caramelized onions over the dough and sprinkle with herbes de Provence. Arrange the anchovies in a lattice pattern and set an olive in each diamond.
Bake for 15 to 20 minutes, until the edges of the crust are golden brown. Let it rest a few minutes on a wire rack before serving.
