Season the shrimp. Sprinkle the shrimp with a pinch each of salt, pepper, and baking soda, if you like. Toss to coat.
Boil the pasta. Bring a large pot of generously salted water to a boil. Cook the spaghetti until al dente according to package directions. Before draining, reserve about a cup of the pasta cooking water. Drain pasta through a colander, but don’t rinse, and set aside.
Sauté the shrimp. While the pasta cooks, heat 2 tablespoons olive oil in a large skillet over medium-high heat. Add them to the skillet in a single layer and cook for about 1 to 2 minutes per side, or until opaque and just cooked through. Transfer the shrimp to a plate and set aside.
Sauté the tomatoes. In the same skillet, lower heat to medium and add the remaining tablespoon of olive oil. Stir in the garlic and cook just until fragrant (about 30 seconds), then add the cherry tomatoes and a pinch of salt. Sauté for 2 to 3 minutes, or until the tomatoes soften somewhat. Add the spinach and stir to wilt. If using, stir in the red pepper flakes.
Combine and toss. Return the shrimp to the skillet along with the cooked pasta. Add the pesto and a splash of the reserved pasta water. Toss everything together gently to coat, adding more pasta water as needed to reach your desired consistency.
Finish and serve. Taste and adjust seasoning with more salt and pepper,. Transfer to a serving bowl and top with grated Parmesan and torn basil, if desired.
Notes
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Baking sodais my secret ingredient for making ultra-tender, snappy shrimp. Just a pinch increases the pH of the shrimp slightly, which helps them stay plump and juicy as they cook. You can skip it if you like.
Try it with sun-dried tomatoes in place of fresh ones for a richer, more concentrated flavor.