Preheat the oven to 350 degrees F. Butter the bottom and sides of an 8×12-inch casserole. (A shallow casserole like a gratin pan is best but not necessary.)

In a food processor or in a bowl and using a mixer, add the flour, baking powder, salt, and all but 2 tablespoons of Parmesan cheese; reserve the 2 tablespoons for later. Pulse together if using a food processor. Whisk together if using a mixer and a bowl.

Add the oil, milk, and eggs and process or beat if using a mixer, until incorporated and a batter has formed. This takes seconds, but stop and scrape if needed.

Spread a third of the batter evenly on the bottom of the dish. Leaving a small border along the edge of the pan clear, alternate layers of deli meat and cheese, starting and ending with deli meat. Gently spread the rest of the batter over the top. Mix the reserved Parmesan and brown sugar and sprinkle over the top.

Bake for about 35 minutes, until the batter looks cooked and golden on top. It should feel firm if gently pressed on the top. Let it rest about 15 minutes before serving. If clean cuts are desired, let cool completely.

Serve warm or at room temperature.

Notes:

• A food processor is preferred; it breaks the parmesan into tiny bits so it’s dispersed through the batter.