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Step 1
Bring a large pot of water to a rolling boil over high heat. Salt it generously. Add the bucatini to the boiling water, reduce the heat to medium-high and cook according to the package directions (for al dente). Reserve 1/2 cup of the cooking water and drain the pasta in a colander set in the sink.
Step 2
In a large skillet over medium heat, heat the oil until shimmering. Add the pancetta and cook, stirring often, until the fat has started to render and the meat is lightly browned and somewhat crispy, 8 to 10 minutes. Carefully pour all but 3 tablespoons of the fat out of the skillet.
Step 3
Add the tomatoes to the skillet and increase the heat to medium-high. Cook, stirring occasionally, until the tomatoes have collapsed and the liquid in the pan has thickened into a sauce, about 15 minutes. Reduce the heat as needed to keep the sauce at a gentle simmer. Taste, and season with salt, as needed.
Step 4
Turn off the heat and cover to keep the sauce warm.
Step 5
Transfer the bucatini to the skillet and gently toss with the sauce, adding a splash or two of the cooking water, as needed, to loosen the consistency.
Step 6
Add the arugula by the handful and continue to toss for about 1 minute, just until the greens are wilted.
Step 7
Divide among individual bowls and sprinkle each portion with the cheese. Serve warm.