Shuck the corn, spritz with oil and salt, and grill over medium heat until kernels start to caramelize and corn has softened.
Once corn has cooled so you can handle it, remove kernels from cob with a sharp paring knife. Set aside.
In a large skillet or other similarly sized pan, heat together the milk, water, salt, cayenne, and garlic powder. Heat until simmering.
Pour in the polenta, and stir until combined. If it clumps up, just press the clumps down with a wooden spoon until they disappear.
Cook the polenta over medium-to-medium low heat until thick enough so that a whisk or spoon pulled through the bottom of the pan leaves a trail.
Add ¾ cup grated Parmesan and stir to blend.
Add baby spinach and stir gently just until the spinach is wilted. Check for thickness: if too thick for your taste, add water in 1/8 cup increments until it gets to where you want it.
Top with grated jack or cheddar cheese, sprinkle with paprika, and cover.
Let polenta sit while cheese melts and polenta continues to absorb moisture, about 5-10 minutes.
To serve: scoop polenta into bowls and top with grilled corn.