Preheat the oven to 350°F and grease a 24-cup mini muffin pan very well (like very well. If you think it's too much, it's good).
In a mixing bowl, beat the butter, granulated sugar, and brown sugar until light and creamy.
Mix in the egg and vanilla until smooth.
Add the flour, baking powder, and salt, and mix on low speed just until a soft dough forms.
In a small bowl, stir together the sugar and cinnamon for the cinnamon sugar coating.
Scoop the dough into 1-tablespoon portions, roll each one in cinnamon sugar, and place them in the mini muffin pan. Gently press the centers down slightly to form little cups.
Bake for 10 to 12 minutes, until the edges are lightly golden and the centers are set. If needed, gently press the centers down again with the back of a spoon right after baking.
Let the cookie cups cool in the pan for 10 minutes, then carefully remove them and transfer to a wire rack to cool completely.
To make the filling, beat the cream cheese and butter until smooth and fluffy. Mix in the powdered sugar and vanilla, then add a little heavy cream or milk if needed until the filling is smooth and pipeable.
Add cream cheese filling to a piping bag with a star tip (I like the Wilton 1M tip). Once the cookie cups are completely cool, pipe or spoon the filling into the centers.
Store churro cookie cups in an airtight container in the fridge.