In a large, heavy-bottomed pot (such as a Dutch oven), heat 1 Tbsp olive oil over medium heat. Add the ground beef and cook over medium heat, stirring as necessary, until cooked through. Using a spoon, spoon of most of the fat/liquid in the pot and then continue cooking the ground beef to brown nicely. Remove ground beef to a bowl and set aside.
Add the remaining 1 Tbsp olive oil to the same pot and heat over medium heat. Add the onion, carrot and celery to the pot and cook, stirring, until the onion is softened, 4-5 minutes. Add the red pepper flakes (if using) and the garlic and cook, stirring, about 1 minute more (don't let the garlic scorch). Add the tomato paste to the pot and cook, stirring, for another 1 minute. Add the red wine, stir, then allow to cook/simmer for about 2 minutes, or until reduced by about half. Add the canned tomatoes, water, basil leaves, oregano, brown sugar and salt. Stir well to combine. Return the cooked ground beef to the pot.
Bring the mixture to a boil, then reduce the heat to medium low and simmer for about 2 hours, stirring regularly and more frequently as the mixture starts to thicken. (*Important to watch closely and stir often as sauce thickens, as the sauce/meat can scorch if is sits on the bottom of the pan in the thicker sauce.) Cook sauce until desired thickness reached. For pasta, I like to leave it a touch thinner. For lasagna or other baked pasta, you can cook until most of the liquid has cooked off.
Add the heavy cream and butter to the sauce and cook, stirring until combined and warmed through. Taste the sauce and add additional salt and/or freshly ground pepper, as needed.
*If desired, you can blend the sauce ever so slightly with a few blitzes with an immersion blender at this point, to blend the onion/carrots into the sauce. This is not necessary, just personal preference if you prefer a chunky or smooth sauce.
Use sauce immediately or cool a bit, then refrigerate or freeze.
Notes
Be sure to read the notes above this Recipe Card, where I share more detailedtips, variations and substitution suggestions for this recipe!