For the dough:
1) Combine the water, yeast, honey, and olive oil in the bowl of an electric mixer fitted with a dough hook. (If the bowl is cold, start with warmer water so it's at least 38°C when you add the yeast.) Add 450g of the flour, then the salt, and mix on medium-low speed. While mixing, add another 150g of flour, or just enough to make a soft dough. Mix the dough on medium-low speed for about 10 minutes, until smooth, sprinkling it with flour to keep it from sticking to the bowl.
2) When the dough is ready, turn it out onto a floured board and knead it by hand a dozen times. It should be smooth and elastic.
3) Place the dough in a well-oiled bowl and turn it to cover lightly with oil. Cover the bowl with a damp kitchen towel. Allow to rest at room temperature for 30 minutes.
For the assembly of the pissaladieres:
1) Preheat the oven to 220°C.
2) Divide the dough into 2 equal parts, rolling each 1 into a smooth ball. Allow the dough to rest for 10 minutes.
3) Roll each dough ball lightly with a rolling pin, then stretch them to 25x38cm rectangles and place on a baking tray sprinkled with cornflour.
4) Spread the tomato paste onto each dough base, leaving a 2cm border all around. Artfully arrange the sliced tomatoes and sliced mozzarella on top. Sprinkle with the cheddar, pepper, and thyme. Brush the edges of the dough with olive oil, and bake for 15 minutes, or until the crust is crisp.
5) Serve hot on a cutting board.