Place the sugar in a large bowl and pour the warm water on top.

Sprinkle the yeast over the surface of the water and allow it to dissolve (approx. 5 minutes).

When the mixture looks foamy (after approx. 5 to 10 minutes), stir in the flour until incorporated.

Stir in the olive oil and salt.

While continuing to mix, add in more flour until the dough gathers itself into a ball and pulls away from the sides of the bowl cleanly. (You may need slightly more or less flour; use your judgement.)

Knead the dough until smooth and elastic.

Cover the bowl with plastic wrap or a damp towel, and allow it to rise in a warm place until doubled in bulk (approx. 45 to 90 minutes).

Punch down the dough and transfer it to a lightly oiled 9x13 baking pan.

Press the dough with your fingertips so it covers the bottom of the pan evenly (if it feels tight and springs back, allow it to rest for 10 to 15 minutes, then try again).

Cover the pan and allow the dough to rise a second time (approx. 45 to 90 minutes).

Preheat the oven to 350 degrees F and dimple the dough with your fingertips.

Bake the crust until puffy and set (approx. 15 minutes).

Heat the olive oil in a large pot over medium heat until shimmering.

Add the onion, carrots, garlic powder, onion powder, Italian seasoning, salt, oregano, and crushed red pepper to the pot.

Cook, stirring, until the vegetables are soft and tender (approx. 5 minutes).

Add the tomato paste and cook, stirring, until browned (approx. 3 to 5 minutes).

Deglaze the pot with balsamic vinegar, scraping with a wooden spoon to bring the fond up off the bottom of the pot and into the sauce.

Add the crushed tomatoes to the pot, turn the heat down to low, place a lid slightly ajar on the pot, and allow the sauce to come to a simmer.

Spoon a thick layer of sauce* over the crust, then bake for another 20 minutes at 350 degrees F.

Cool completely, then sprinkle with pecorino romano.

Cut the tomato pie into squares and serve cold or at room temperature.