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Step 1
Trim and cut 8 medium zucchini crosswise into rounds of different thicknesses (1/4 to 1/2-inch thick). Layer in a colander, seasoning each layer with a generous pinch of kosher or coarse sea salt. Set aside to rest for 30 minutes.
Step 2
Rinse the zucchini, then pat dry with paper towels or a clean kitchen towel.
Step 3
Heat 1 cup olive oil in a large skillet over medium heat until shimmering. Add a quarter of the sliced zucchini in a single layer, but do not stir. Every 2 to 3 minutes, add another quarter of the zucchini, layering them without stirring. Once all the zucchini has been added, cook, gently stirring every few minutes, until the zucchini range in color from light gold to dark golden brown, and in texture from soft to crisp, 20 to 25 minutes total. Season with crushed Tellicherry black peppercorns.
Step 4
While the zucchini is cooking, bring a large pot of salted water to a boil. Add 1 pound dried spaghetti, letting it soften and submerge itself in the water. Once the pasta is submerged, give it a stir so it doesn’t stick on the bottom. Cook to al dente, about 1 minute less than the package instructions.
Step 5
Reserve 1/2 cup of the pasta cooking water. Drain the spaghetti and immediately add it to the zucchini. With the heat still on medium, add 2 tablespoons of the pasta cooking water, sprinkle with 1 cup grated Pecorino Romano cheese, and, using tongs, gently lift and toss the spaghetti to mix well. If the sauce is looking a little thick, add another splash or two of pasta cooking water. Season with more salt and pepper as needed. Bring the skillet to the table and serve immediately.