Preheat the grill over indirect/medium-high heat to 400 degrees F.
Mix together the flour and cornmeal, and then add the baking powder, salt and sugar and whisk until well combined using a wire whisk. Whisk together the milk, oil and eggs in a separate bowl. Add the wet ingredients into the dry ingredients and mix until just combined, and then stir in the creamed corn until just combined (do not over-mix).
Distribute the butter over the skillet and preheat on the grill or in the oven until hot and the butter is melted. Pour the cornbread batter directly into the warm skillet and transfer immediately to the center of the grill grate. Cover the grill and cook until a toothpick inserted into the center comes out clean, 35 to 40 minutes.
Serve from the pan while still warm with the Sweet Strawberry Butter.
Mash or stir the butter until smooth and slightly fluffy. Stir in the jam, brown sugar, salt and lemon zest, mashing with the back of a fork until smooth and all the ingredients are incorporated. Taste for seasoning.
Drop the butter in spoonfuls onto a piece of parchment or plastic wrap, and then roll up and smooth out to form a round log. Refrigerate until hard and easy to cut into pieces. The butter can be made in advance and stored tightly covered in the refrigerator for up to 1 week and in the freezer for up to 3 months. Yield: 1/2 cup.