Fill a deep fryer with correct amount of vegetable oil, according to manufacturer's instructions. Set fryer to heat oil to 400 degrees. Mix Jell-O Cheesecake according to directions, minus 1/4 cup milk. Add softened Philadelphia Cream Cheese. Mix well.
Place 2-3 heaping tablespoons of cheesecake mix in center of fresh tortilla. Fold tortilla burrito style and place in basket. Put as many chimichangas in basket as you can without them touching. Place a smaller basket over them for light pressure so they do not puff up during frying.
Place in fryer for several minutes, until light to golden brown. Remove from oil and carefully place directly on cooling rack. Immediately sprinkle with cinnamon sugar and let cool.