In a mixing bowl, combine the softened cream cheese, powdered sugar, and vanilla extract. Use a fork or an electric mixer to blend until smooth.
Gently fold in the diced strawberries into the cream cheese mixture until evenly distributed.
Lay out a tortilla on a clean surface. Place about ¼ cup of the strawberry cheesecake filling in the center of the tortilla.
Fold the sides of the tortilla inwards over the filling, and then roll it up tightly from the bottom to the top to form a chimichanga. Repeat this step for all tortillas.
In a large skillet or deep fryer, heat the vegetable oil over medium heat until it reaches 350°F (175°C).
Carefully place 2 to 3 chimichangas into the hot oil at a time, frying them until they are golden brown and crispy, about 2-3 minutes per side.
Use a spatula to remove the chimichangas from the oil and place them on paper towels to drain excess oil.
While still warm, roll the chimichangas in cinnamon sugar to coat them evenly.
Serve warm, garnished with additional strawberries or whipped cream if desired.