In a medium bowl, combine the sliced strawberries, granulated sugar, and vanilla extract. Toss to coat and set aside to macerate for about 15 minutes.
In another bowl, beat together the softened cream cheese, powdered sugar, and lemon juice until smooth and creamy.
Spread a generous layer of the cream cheese mixture on four slices of bread. Top each with a portion of the macerated strawberries and then place another slice of bread on top to create a sandwich.
In a shallow dish, combine the crushed graham crackers, flour, baking powder, and salt.
In a separate bowl, whisk together the egg and milk until well combined.
Heat about 2 inches of vegetable oil in a deep skillet or pot over medium heat until it reaches 350°F.
Dip each sandwich into the egg mixture, allowing any excess to drip off, then coat it in the graham cracker mixture, pressing gently to adhere.
Carefully place the coated sandwiches into the hot oil, frying in batches for about 2-3 minutes per side or until golden brown. Remove and drain on paper towels.
Dust the fried sandwiches with powdered sugar before serving.