Score the tops of the cherry tomatoes with an “X,” then boil briefly until skins loosen (about 30 seconds). Transfer to cold water to stop cooking. Peel and slice each tomato into thirds. Set aside.
Season shrimp with salt and black pepper. In a large pan, heat olive oil over medium heat. Add shrimp and cook until just starting to turn pink—don’t fully cook. Remove and set aside.
In the same pan, add a bit more olive oil if needed. Add sliced garlic and whole basil stems. Sauté gently over medium heat for a few minutes, ensuring garlic doesn’t brown.
While the garlic and basil cook, start boiling your spaghetti in salted water. When it’s almost halfway cooked, add a ladle of pasta water to the pan with garlic and basil. Simmer gently. Remove basil stems after a couple minutes.
Add a squeeze of fresh lemon juice and red pepper flakes to the pan. Drop in the spaghetti about 3 minutes before it reaches al dente (it will finish in the pan). Stir gently to coat and add more pasta water as needed.
Toss in the sliced cherry tomatoes and hand-torn basil leaves. Stir well to create a light sauce as the olive oil emulsifies with the pasta water.
Once spaghetti reaches al dente, return the shrimp to the pan. Stir gently and cook just until the shrimp is fully done.
Serve the spaghetti with shrimp, spooning over the tomato-basil sauce. Garnish with extra basil leaves and red pepper flakes to taste.