Preheat oven to 400 degrees.
Lay the quartered tomatoes on a large baking sheet. Drizzle with 1 tablespoon of olive oil and sprinkle with salt and pepper.
Roast the tomatoes in the oven for 30-35 minutes, or until the tomatoes are golden on top.
While the tomatoes are roasting, heat a large sauce pot over medium high heat and add 2 tablespoons of olive oil. Once heated, add the onions and cook over medium heat, stirring occasionally, until the onions have turned translucent and begun to caramelize. Reduce the heat to low and continue cooking and stirring occasionally until they turn a deep, rich, golden hue, or about 20 minutes total.
Once the onions are caramelized, add the garlic and saute until the garlic is soft, about 2-3 more minutes, then remove from heat until the tomatoes are finished roasting.
Once the tomatoes have roasted, remove from the oven and transfer them to the pot with the onions, discarding any watery tomato juice. Mix with a spatula, then use an immersion blender (or carefully transfer to a blender or food processor in batches) and blend until there are no large chunks.
Add the sugar, basil, bay leaves, onion powder, salt, baking soda and balsamic vinegar and stir to combine, then return to heat and simmer for 20-30 minutes to reduce slightly and to combine the flavors. Taste and season with more salt and pepper if desired.
Use immediately, or cool completely and transfer to an airtight container to store in the fridge or freezer.