How to Make It
In a small bowl, stir the yeast into the water and set aside until foamy, about 5 minutes. Put 1 1/2 cups of the flour in a large bowl and make a well in the center. Add the egg and olive oil to the well and start to incorporate the flour. As you mix, stir in the dissolved yeast. Continue mixing until a supple bread dough forms; you may need to add a little more flour or water as you mix.
Transfer the dough to a lightly floured work surface and knead for a few minutes, until silky smooth. Transfer the dough to a lightly oiled bowl, cover lightly with plastic wrap and set aside while you make the topping.
In a heavy saucepan or casserole, cook the onions and garlic in the olive oil over low heat, stirring often, until thoroughly softened and lightly golden, about 20 minutes. Add the chopped tomatoes and cook, stirring often, until the mixture is very thick, about 15 minutes. Season with salt and pepper and let cool.
Preheat the oven to 400°. Divide the dough into 2 pieces and roll each piece out to an 8-inch round about 1/4 inch thick. (The rounds need not be regular in shape; in fact, irregularity is part of the charm.) Transfer each round to a lightly oiled cookie sheet.
Pinch around the edges of the dough to make very slightly raised borders. Spread the onion mixture over both dough rounds. On 1 tart, arrange the anchovy fillets in a lattice pattern and set the olives within the squares. On the other tart, scatter the sliced tomatoes and basil. Sprinkle both tarts with salt and pepper and bake in the center of the oven for about 25 minutes, or until the crusts are golden around the edges and the toppings are bubbling and beginning to brown. Cut into wedges and serve hot or at room temperature.