Bring a large pot of salted water to a rolling boil and add the spaghetti, stirring occasionally to prevent sticking. While the pasta cooks, prepare your mise en place: thinly slice the garlic, remove the kale stems and tear the leaves into bite-sized pieces, finely chop the parsley, and measure out the lemon juice and zest. When the pasta reaches al dente (usually 1-2 minutes before the package time), reserve 1 cup of the starchy pasta water in a measuring cup, then drain the pasta in a colander.
Heat the olive oil in a large skillet over medium heat. Once the oil is shimmering, add the thinly sliced garlic and red pepper flakes, cooking for just 30-60 seconds until fragrant but not brown—burnt garlic tastes bitter, so watch carefully. I like to listen for a gentle sizzle; once you smell that toasty garlic aroma, it's time to move forward.
Add the torn kale, salt, and freshly ground black pepper to the hot oil and garlic. Toss constantly for about 1 minute until the kale is wilted and softened. The residual heat from the oil and the moisture released by the kale will cook it perfectly without turning it mushy.
Add the drained pasta to the skillet along with 1/2 cup of the reserved pasta water, lemon juice, and lemon zest. Toss everything together over medium heat for about 1-2 minutes, allowing the starchy pasta water to emulsify with the oil and coat each strand. The pasta water is crucial here—it creates a silky sauce that clings to the noodles. If the mixture looks too dry, add more reserved pasta water a splash at a time until you reach a light, glossy consistency.
Remove from heat and stir in the fresh parsley and smoked paprika. Taste and adjust seasoning with additional salt and pepper if needed. I find the smoked paprika adds a subtle depth that rounds out the bright lemon notes. Divide among bowls and top generously with grated Parmesan cheese. Serve immediately while hot.