Meanwhile, melt the butter in a large skillet
over medium-high heat. Add the onion, carrots,
garlic, 1/4 teaspoon salt and a few grinds of
pepper. Cook, stirring occasionally, until
softened, 6 to 8 minutes. Add the ground beef,
1/4 teaspoon salt and a few grinds of pepper
and cook, breaking up the meat, until no longer
pink, about 4 minutes. Add the tomato paste and
cook until evenly combined, 1 minute. Add the
wine and simmer until almost completely dry, 1
to 2 minutes. Add 1/2 cup of the reserved
cooking water, the tomatoes and half the basil.
Bring to a boil, then reduce the heat to a
simmer and cook until the tomatoes start to
burst and the mixture is saucy, 4 to 7 minutes.