In a large mixing bowl, whisk together the flour, sugar, baking powder, and salt until evenly combined. In a separate bowl, beat the eggs, then add the milk, melted butter, and vegetable oil. Pour the wet ingredients into the dry ingredients and gently mix until just combined with a few lumps remaining.
In a small bowl, stir together the brown sugar and ground cinnamon to create the cinnamon-sugar filling. Measure out a portion of this mixture to set aside for topping after cooking.
Preheat a griddle or large skillet over medium heat until hot but not smoking. Lightly grease with butter or non-stick spray. Pour approximately 1/4 cup of batter for each pancake onto the skillet. Spoon about one teaspoon of cinnamon-sugar mixture onto the center of each pancake, then cover with a small amount of batter to encase the filling.
Cook the pancakes for 2-3 minutes, or until bubbles form on the surface and the edges look set. Carefully flip with a spatula, then cook for an additional 2-3 minutes until golden brown on both sides. The pancakes should be fluffy and slightly crisp on the exterior.
Once cooked, transfer the pancakes to a serving plate. Optional: dust with a little powdered sugar or drizzle with syrup. Serve warm, showcasing the cinnamon swirl pattern inside each pancake.
