Heat the butter in a deep saucepan over medium heat. Add the onion, celery, and black pepper. Cook for 2 minutes, then reduce heat to medium-low. Add thyme, scallions, salt, pimento peppers, and garlic.
After 3 minutes, stir in the grated nutmeg and cook for 1 more minute.
In a blender, puree 1/2 cup of the milk with 1/2 cup of the corn kernels and the honey to make corn milk. As explained in the Corn Pie recipe video below, the honey will further enhance the natural sweetness of the fresh sweet corn. Add the remaining kernels to the pot and stir well. Turn the heat back to medium and add the corn milk and the remaining evaporated milk, then bring to a gentle simmer. Here's where you'll add the grated carrot for a bit of added texture and sweetness.
Once small bubbles appear, stir in the cornmeal and half of the cheese. Mix well to combine.
Transfer mixture to a greased baking dish and top with the remaining cheese.
Bake uncovered in a preheated 350°F (175°C) oven for 30–40 minutes, depending on thickness.
Look for a firm set with a golden cheesy top.
Allow to cool for 10–15 minutes before slicing and serving.