I think this would work with just about any quick bread or dense cake recipe but carrot cake is the only one I have tried and I don't know if I can stray now it's so good.
My personal carrot cake recipe is too light and airy for this application so I searched around to find a recipe that looked dense. The recipe that follows is from Martha Stewart and is called a tea cake. It is baked in a loaf pan and is dense but still very moist - and delicious!
I used my own cream cheese frosting recipe not the one from MS.
Step 1: For the Carrot Cake
1/2 cup (1 stick) unsalted butter, room temperature, plus more for pan (and grilling)
1 1/4 cups all-purpose flour (spooned and leveled), plus more for pan
1 teaspoon baking powder
1/2 teaspoon baking soda
1/2 teaspoon salt
1/2 teaspoon ground cinnamon
1/2 teaspoon ground nutmeg
1/2 cup packed dark-brown sugar
2 large eggs
1 1/2 teaspoons pure vanilla extract
1 cup packed grated carrots (from about 2 carrots)
Preheat oven to 350 degrees. Butter and flour a 5-by-9-inch (6-cup) loaf pan. In a bowl, whisk together flour, baking powder, baking soda, salt, cinnamon, and nutmeg.
Using an electric mixer, beat butter and brown sugar until light and fluffy; beat in eggs and 1 teaspoon vanilla. Beat in carrots. With mixer on low, gradually add flour mixture; beat just until combined. Transfer batter to prepared pan; bake until a toothpick inserted in center comes out clean, 40 to 45 minutes. Let cool in pan 5 minutes. Turn cake out onto a wire rack, and let cool completely.
** I used a wide loaf pan and baked it for 30 minutes and it came out perfect.
Step 2: For the Cream Cheese Frosting
4 oz cream cheese
4 T. butter
1 t. vanilla extract
1 T. maple syrup
2 c. powdered sugar - give or take depending on desired thickness
In a medium mixing bowl combine cream cheese and butter until smooth. Add vanilla and maple syrup and stir to combine. Gradually add powdered sugar until you have a desired thickness.
Step 3: Grill and Frost
Once your cake has cooled completely cut 1/2 inch slices. Spread one side with a thin layer of butter. Place buttered side down on the heated grill. Close griddler and grill approximately 2-3 minutes and remove from heat and let cool on a wire rack.
Smear unbuttered side of one piece of cake with cream cheese frosting and top with another grilled slice of cake. Cut if preferred and serve! It's a delightful experience!!