Preheat 2-3 inches of oil to 350°F in a saucepan or deep fryer. Line a large plate with paper towels and set aside.
In a medium bowl, add the cream cheese, sour cream, sugar, lemon zest and vanilla. Beat until smooth and then gently fold in the sliced strawberries.
Lay a flour tortilla on a work surface. Spread a large spoonful of the cheesecake filling onto the lower third of the tortilla. Roll up the tortilla as if it were a burrito, tucking in the edges. Then seal with a toothpick or use a paste of flour and water along the seams to hold it all together. Repeat with the remaining tortillas.
Using kitchen tongs, carefully place one chimichanga into the hot oil. Deep fry for 3-4 minutes until golden, turning occasionally. Remove to the prepared plate and repeat with the remaining chimichangas.
Add the cinnamon sugar to a plate. Roll each chimichanga in the cinnamon sugar until nicely coated. Serve with additional fruit, ice cream, and caramel or chocolate sauce.