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In a large pot on medium heat, heat a couple tablespoons of olive oil, and add the onions, garlic, and carrots. Add a generous pinch of salt and cook, stirring occasionally, for around 15 minutes, until slightly browned.
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Add the meat to the pot, breaking it up into small chunks with a wooden spoon or spatula.
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Cook meat and vegetables together until meat is browned and/or cooked through. If there’s a lot of liquid in the pot, the meat may not brown easily. That’s fine.
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Fold tomato paste into the beef mixture and cook for another 5 minutes, continuing to incorporate into the other ingredients.
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Add the red wine, thyme, and bay leaves to the pot, plus two cups of water.
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Simmer the bolognese until liquid boils down by around 1/3 - around 45 minutes - then add two more cups of water. Taste the sauce frequently, seasoning with salt and pepper as desired.
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Simmer until sauce is rich and thick, then remove from heat. Remember that the sauce will thicken more when it cools.
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While sauce is simmering around 20 minutes after the second water addition, set the pasta on to boil. Reserve 1/3 cup pasta water at end of cooking.
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Drain cooked pasta and return to pot. Ladle desired amount of bolognese over pasta, add pasta water, and cook over medium heat until water is reduced.
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Serve with cheese and olive oil, if you want.