To a medium to large skillet or Dutch oven, set over medium heat, add the butter. When melted, add the corn kernels, shallot and garlic. Cook until the shallot has softened, about 2 to 3 minutes. Add the cayenne, salt and heavy cream; cover the pot to cook for about 5 to 6 minutes.
Meanwhile, bring a pot of salted water to a boil. Add the pasta and cook until al dente (mine took about 8 to 9 minutes). Scoop out about 1 cup of pasta water and set it aside. Drain the pasta and set aside.
To the corn mixture, add 3/4 cup reserved pasta water, juice from 1 lime and mix. Cook until warmed, about 1 minute. Add the pasta, the crumbled cotija cheese and toss until combined. If you need to, add a bit more pasta water or cream. Give it a taste and adjust the salt to your liking (it should be ok!).
Divide amongst bowls or plates and garnish with a bit more cotija cheese and some leaves of cilantro.