In a mixing bowl, beat the softened cream cheese with the powdered sugar and vanilla extract until smooth and creamy.
Lay out the slices of bread on a clean surface. Spread the cream cheese mixture evenly over 4 slices. Top with sliced strawberries and cover with the remaining 4 slices of bread to create sandwiches.
Use a bread knife to trim the edges, if desired, to create a neat sandwich shape. Press the edges slightly to seal.
Prepare a coating station: Place the flour in a small bowl, beat the egg in another bowl, and put the breadcrumbs in a third bowl.
Heat oil in a frying pan over medium heat until it reaches 350°F (175°C).
Dredge each sandwich first in the flour, then dip in the beaten egg, and finally coat with breadcrumbs. Ensure each sandwich is evenly coated.
Carefully place the sandwiches in the hot oil and fry for about 2-3 minutes on each side, or until golden brown.
Remove the sandwiches with a slotted spatula and drain on paper towels.
Serve warm, optionally dusted with powdered sugar. Enjoy your fried strawberry cheesecake sandwiches!