Cook the pasta according to the package directions. Reserve 1/2 cup of cooking liquid, set aside, + drain.
Meanwhile, heat the oil in a large skillet over medium-high heat. Add the leeks, garlic, 1/2 teaspoon salt, + 1/4 teaspoon pepper. Cook, stirring occasionally, until tender, 3 to 4 minutes.
Add the corn + wine. Simmer until the corn is tender, 2 to 3 minutes.
Stir in the half-and-half. Add the pasta, season with 1/2 teaspoon salt + 1/4 teaspoon pepper, + toss to combine. Fold in the arugula. If needed, add a little of the reserved pasta cooking liquid to achieve your desired consistency (i only added about 1/8 cup). Add more salt/pepper if needed.
Sprinkle with the pecorino or parmesan immediately before serving.