Mix cream cheese, powdered sugar, and vanilla until smooth. Gently fold in diced strawberries.
Using a rolling pin, flatten each slice of bread until thin (this helps them roll without cracking).
Spread about 2 tablespoons of the cream cheese mixture onto each flattened bread slice, then roll up tightly like a little burrito.
In a shallow bowl, whisk together eggs and milk. In another bowl, combine granulated sugar and cinnamon.
Dip each roll in the egg mixture, then roll in the cinnamon-sugar mixture to coat completely.
Place rolls seam-side down in a greased 9x13-inch baking dish. Drizzle with melted butter. Cover and refrigerate overnight.
In the morning, preheat oven to 375°F. Bake uncovered for 22-25 minutes until golden and crispy.
Let cool for 5 minutes, then dust with extra powdered sugar before serving.