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Step 1
Stir 3 1/2 cups water, 1 1/2 cups tomato purée, and 1 1/2 teaspoons kosher salt together in a medium saucepan. Bring to a simmer over medium heat. Adjust the heat to maintain a gentle simmer.
Step 2
Heat 2 tablespoons olive oil in a 12-inch or larger nonstick or cast iron skillet over medium heat until shimmering. Stir in 2 minced garlic cloves and cook, stirring occasionally, until very fragrant, about 1 minute. Stir in 1 tablespoon tomato paste and 1 teaspoon red pepper flakes, and cook until darkened in color, 2 to 3 minutes. Stir in just enough of the tomato broth to cover the bottom of the skillet (about 1/2 cup).
Step 3
Increase the heat to medium-high. Arrange 8 ounces dried spaghetti across the bottom of the pan in an even layer. Pour 1 1/2 cups of the tomato broth over the spaghetti. Use tongs to move the spaghetti as needed so it’s evenly coated and partially submerged. Cook undisturbed until the broth is mostly absorbed and the spaghetti sticks to the pan, 5 to 6 minutes. Flip with tongs or a thin spatula so that the bottom layer is on top.
Step 4
Continue incrementally adding the tomato broth 1 cup at a time, arranging the spaghetti as needed so it's evenly coated. After each addition, cook undisturbed until the liquid is mostly absorbed and the spaghetti sticks to the pan, 3 to 5 minutes. Flip with tongs so that the bottom layer of spaghetti is on top before adding the next cup of broth.
Step 5
Repeat cooking, flipping, and adding broth until the spaghetti is al dente, sticks to the bottom of the pan, and is slightly charred. The total cooking time will be 17 to 24 minutes from when you first started adding broth. Taste and season with more kosher salt as needed.