Combine the pumpkin puree, evaporated milk, sugar, egg and pumpkin pie spice in a medium bowl. Mix well.
Unroll one can of the crescent rolls into a rectangle. Pinch the diagonal seams together. Using a pizza cutter, cut the rectangle into 16 squares. Press each of the squares into an ungreased mini muffin tin, folding the edges over as needed to make a cup.
Fill each of the cups with the pumpkin mixture. Transfer to the oven and bake until the cups are golden brown and the filling is set, about 20 minutes. Let cool for 10 minutes.