Preheat the oven to 425°F and grease a 9x13-inch baking pan.
In a small bowl, whisk together the melted butter, brown sugar, ground cinnamon, and flour for the cinnamon swirl mixture. Set aside to thicken slightly while you prepare the pancake batter.
In a medium bowl, combine the flour, baking powder, baking soda, and salt.
In a separate large bowl, whisk together the eggs and melted butter until smooth. Add in the milk, maple syrup, and vanilla extract, whisking until fully combined.
Add the dry ingredients to the wet ingredients and mix until just combined. Do not overmix. Let the batter rest for 5 minutes. This helps the flour hydrate and gives the pancakes a fluffier texture.
After 5 minutes, give the batter a gentle stir, then pour it into the prepared baking dish and spread evenly. Transfer the cinnamon swirl mixture to a piping bag or small zip-top bag with the corner snipped off. Pipe swirls all over the top of the pancake batter.
Bake for 12 to 15 minutes, or until the center is set and the top is lightly golden. For an optional glaze, whisk together the softened cream cheese, powdered sugar, and milk until smooth. Spread or drizzle over the warm pancakes, then slice into squares and serve.