For the pasta: Bring a large pot of salted water to a boil over high heat. Add the pasta and cook until tender but still firm to the bite, stirring occasionally, about 8 to 10 minutes. Drain pasta, reserving 1 cup of the cooking liquid.

Meanwhile, in a large, heavy skillet warm the olive oil over medium heat. Add the shallots and garlic and cook for 2 minutes. Add the shrimp and cook until pink, about 5 minutes. Add the cooked linguine, lemon juice, lemon zest, salt, and pepper. Toss to combine. Turn off the heat and add the arugula. Add the lemon oil to the pasta and toss to combine. Add some of the cooking water to desired consistency. Add the chopped parsley to the pasta and toss to combine. Taste and adjust seasoning if necessary, and serve.

*If making lemon-infused oil from scratch, combine 1/2 cup olive oil and the zest from one lemon in a small bowl and reserve.