Mix softened cream cheese, powdered sugar, and vanilla extract until smooth and creamy.
Spread the cream cheese mixture on four slices of bread. Add sliced strawberries and a spoon of strawberry jam. Top with the remaining bread to form sandwiches and press gently.
Whisk together flour, milk, egg, vanilla, sugar, and a pinch of salt until the batter is smooth and lump-free.
Pour about 2 inches of oil into a skillet or pot. Heat it to 350°F (175°C).
Dip each sandwich fully into the batter, then fry for 2–3 minutes per side until golden and crispy.
Place on paper towels to remove excess oil. Drizzle with sweetened condensed milk if desired. Cut in half and enjoy warm!