Bring a large pot of water to a boil and cook the pasta according to package instructions.
In the meantime, heat a large skillet over medium-high heat. Add the butter and let melt. Brown lightly. Add the minced shallot and cook for a minute.
Add corn to the skillet and cook for 3 minutes to caramelize. Add garlic, salt, pepper, and thyme. Cook for 2 more minutes.
Ladle out 1 ½ cup of pasta water and add it to the skillet. Add the heavy cream, reduce the heat to medium and bring to a simmer to thicken the sauce.
Drain the pasta and add it to the skillet along with parmesan cheese. Cook for 1 minute and stir well to coat the pasta. Adjust seasoning if necessary.
Serve immediately. Garnish the dish with more parmesan and thyme if you prefer.