01 - Combine softened cream cheese, sugar, vanilla extract, and sour cream in a medium mixing bowl. Beat with hand mixer or whisk until completely smooth and creamy, approximately 2 minutes. Set aside.
02 - Lay flour tortillas on a clean work surface. Spoon approximately 2 tablespoons of cheesecake filling onto the lower third of each tortilla. Top with 1 tablespoon diced berries if desired. Fold both sides inward toward the center, then roll tightly from bottom to top to form a secure burrito shape. Insert toothpicks through the seam to prevent unraveling during frying.
03 - Pour vegetable oil into a deep skillet or heavy-bottomed saucepan to a depth of 2 inches. Heat over medium-high heat until oil reaches 350°F. Use a deep-fry thermometer to monitor temperature accuracy.
04 - Carefully place 2-3 chimichangas in the hot oil, seam side down. Fry for 2-3 minutes until golden brown and crispy, then flip and fry the opposite side for an additional 2-3 minutes. Remove with a slotted spoon and transfer to a paper towel-lined plate to drain excess oil. Repeat with remaining chimichangas.
05 - Working quickly while chimichangas are still hot, brush each fried tortilla generously with melted unsalted butter. Ensure even coverage on all sides for optimal cinnamon sugar adhesion.
06 - Combine granulated sugar and ground cinnamon in a shallow dish, mixing thoroughly to blend. Roll each buttered chimichanga in the cinnamon sugar mixture, pressing gently to ensure complete and even coating on all surfaces.
07 - Arrange chimichangas on a serving platter. Serve immediately while warm and crispy. Offer optional garnishes including whipped cream, fresh berries, or chocolate sauce for enhanced presentation and flavor.