Preheat your oven to 375°F (190°C) and grease a 9x13-inch baking dish or a 9-inch round cake pan with butter or cooking spray.

In a blender, combine the eggs, vegetable oil, whole milk, grated Parmesan cheese, and salt, then blend on high speed for about 1 minute until smooth and frothy.

Add the all-purpose flour and baking powder to the blender, pulsing just until the batter is smooth and no flour pockets remain.

Pour half of the blender batter into the prepared baking dish, spreading it evenly to cover the bottom of the pan.

Layer the sliced ham evenly over the batter, followed by a layer of the sliced mozzarella cheese, covering the entire surface.

Pour the remaining batter evenly over the ham and cheese layer, using a spatula to gently spread it to the edges, then sprinkle dried oregano over the top.

Bake in the preheated oven for 30 to 35 minutes, or until the top is puffed, golden brown, and a toothpick inserted into the center comes out clean.

Let the pie cool in the pan for 10 minutes before slicing into squares and serving warm or at room temperature.