Bring a large pot of salted water to boil.

Meanwhile, in a large cast iron or non-stick skillet, heat the olive oil over a medium flame. Saute the onions until al dente, about 5 minutes. Add the garlic and red pepper flakes and cook for another minute.

Coarsely chop the beet greens into strips about 1 to 2 inches wide. Add the greens to the pan along with the sugar, salt, and water. Turn the heat up to medium-high and cook the greens, stirring occasionally, until wilted, about 3 minutes. Add the cherry tomatoes and stir to combine. Simmer the mixture until most of the liquid has evaporated, then stir in the vinegar and lemon juice. Continue to cook, stirring occasionally until the tomatoes have begun to soften, wrinkle, and release their juices, about 10 minutes.

Cook the pasta according to package directions until al dente. Reserve 1/4 cup of cooking water. Drain the pasta and add to the pan with the greens. Toss to combine, adding a splash of cooking water if necessary to create more of a sauce.

Ladle the pasta into two bowls and garnish with a generous glug of olive oil and some grated pecorino, if that's your bag.