Heat 1 tablespoon olive oil in a wide pot over medium heat. Once hot, add the diced onion and cook for 6 minutes until soft. Add the roasted garlic paste and cook for 1 minute until fragrant.
Add the tomato paste and mash into the garlic and onion for 2–3 minutes until it deepens in color and begins to stick to the bottom of the pot.
Pour in the red wine and stir to incorporate the tomato paste. Bring to a boil. Reduce the heat and add the reserved mushroom-soaking liquid.
Add the whole peeled tomatoes and thyme sprigs. Add a generous pinch of salt, sugar, and black pepper to taste. Bring to a boil. Reduce the heat to low and cover. Simmer for 1 hour, stirring periodically to ensure the sauce does not stick.
After 1 hour, remove the lid and taste the sauce. Add more salt, pepper, or sugar if needed.
Using a potato masher, mash the tomatoes to break them up. Continue simmering on low heat until the sauce is thick.