Preheat the broiler. Heat the olive oil in a medium ovenproof nonstick
skillet over medium-high heat. Add the onion and carrot and cook,
stirring occasionally, until softened, about 5 minutes. Add the garlic
and cook until softened, 1 minute. Add the beef, 1/2 teaspoon salt
and a few grinds of pepper and cook, stirring occasionally, until no
longer pink, about 4 minutes. Add the tomatoes with their juices,
oregano, 1/4 teaspoon salt and a few grinds of pepper. Bring to a boil,
then reduce the heat to a simmer and cook until the sauce thickens,
15 to 20 minutes.
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Meanwhile, bring a large pot of salted water to a boil. Add the
gnocchi and cook as the label directs. Reserve 1/4 cup cooking water,
then drain. Toss the gnocchi with the butter and reserved cooking
water in a large bowl until coated; stir in the parsley and season with
salt and pepper.
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