Step 1: Heat olive oil in a large pot or Dutch oven over medium heat. Add the finely diced onion and sauté until softened and translucent, about 5-7 minutes.
Step 2: Add the minced garlic and diced bell pepper (if using) to the pot. Sauté for another 3-5 minutes, until the bell pepper starts to soften and the garlic is fragrant, being careful not to burn the garlic.
Step 3: If using ground meat, add it to the pot now. Break it up with a spoon and cook until browned, draining any excess fat. Skip this step if making a vegetarian sauce.
Step 4: Pour in the jarred pasta sauce. Stir well to combine all the sautéed aromatics and meat. Add the vegetable or chicken broth, tomato paste, dried oregano, dried basil, red pepper flakes, and bay leaf. Stir thoroughly.
Step 5: Bring the sauce to a gentle simmer. Once simmering, reduce the heat to low, cover the pot, and let it cook for at least 30 minutes, or up to an hour for deeper flavors, stirring occasionally.
Step 6: Remove the bay leaf. Stir in the fresh basil, fresh parsley, and heavy cream or mascarpone (if using). Taste and adjust seasonings, adding salt and black pepper as needed. Add a pinch of sugar if the sauce tastes too tart.
Step 7: Serve your doctored pasta sauce hot over your favorite pasta, or use as a base for other dishes like lasagna or chicken parmesan. Garnish with fresh Parmesan cheese and an extra drizzle of olive oil, if desired.