Roast tomatoes - Preheat the oven to 380 F. Place halved tomatoes in a bowl with minced garlic and diced shallots. Pour in olive oil, sprinkle with salt, pepper and dried herbs. Pour into 9x13 pan spread out in a single layer. Cover the baking dish with foil. Bake for 40 minutes. Then remove the foil, reduce the temperature to 340 and bake for another 15 minutes until lightly browned, roasted.
In a large pot or Dutch oven, heat olive oil over medium heat. Add the chopped onion and sauté until translucent, then add 1 ea. minced carrot, and celery (optional). Cook for another 3-4 minutes until the vegetables soften. Add the ground beef to the skillet, breaking it apart with a spatula. Cook until browned and no longer pink.
On a cutting board, chop roasted cherry tomatoes (as much as you desire, or leave as is for larger pieces). OR put into a blender if you want your sauce to be smooth but with the roasted flavor.
Add chopped or pureed tomatoes into your pot with tomato sauce, tomato paste, dried oregano, basil, thyme, salt, and pepper. Adjust consistency with more tomato sauce for thinner or more paste for thicker.
Reduce heat to low, cover with a lid and let the sauce simmer for 15-25 minutes, allowing the flavors to meld together. Adjust seasoning to taste.