In a bowl, beat cream cheese, sour cream, sugar, and vanilla until smooth. Fold in ¾ cup sliced strawberries.
Spoon filling onto the lower third of each tortilla. Fold in the sides and roll up tightly like a burrito. Secure with toothpicks.
Mix cinnamon and sugar in a shallow bowl. Line a plate with paper towels for draining.
Pour 2 to 2½ inches of vegetable oil into a saucepan. Heat over medium-high until it reaches 360ºF.
Fry a few at a time for 2–3 minutes, turning until golden brown and crisp on all sides.
Drain briefly on paper towels, then roll warm chimichangas in the cinnamon-sugar mixture.
Remove toothpicks and serve warm with extra sliced strawberries on top or on the side.