Fill a stockpot halfway with water and bring to a boil over high heat. Add the milk, sugar
, the 3 tablespoons butter, and some salt and pepper to the boiling water. Add the corn and boil for 15 minutes; remove and pat dry.
Prepare a grill or grill pan for medium-high heat. Place the corn (husks on) on the grill and cook, turning occasionally, to lightly char the kernels, about 5 minutes.
Meanwhile, in a medium bowl, mix together the softened 8 tablespoons butter and the garlic powder, smoked paprika, lime zest and some salt and pepper.
Peel back the corn husks to expose the kernels. Using a pastry brush, brush the grilled corn with the butter mixture evenly on all sides. Sprinkle generously with the Cotija. Serve.