Whisk flour, baking powder, and salt in one bowl, then mix milk, oil, and eggs in another and combine gently until slightly lumpy.
Stir melted butter, brown sugar, and cinnamon until thick, then transfer to a piping bag or snipped zip-top bag.
Preheat a lightly greased griddle to 325°F so the pancakes cook evenly.
Pour batter onto the griddle, pipe a cinnamon swirl on top, and cook until bubbles form, then flip and cook until golden.
Melt butter and cream cheese together, then whisk in powdered sugar and vanilla, adding milk if needed for a pourable glaze.
Stack pancakes and drizzle generously with cream cheese glaze, serving warm.