Heat a skillet or griddle over medium heat. Add butter to melt.
Prepare your dipping station: In a small pan or dish, whisk together milk, egg, and vanilla extract. On a plate or small pan, place pulverized cookie crumbs and pat into one layer. Set aside.
In a small bowl, beat together softened cream cheese with powdered sugar, lemon zest. Gently fold in chopped strawberries.
Spread filling onto 2 slices of bread, dividing the mixture evenly. Top each piece with another piece of bread to make a "sandwich".
Quickly dunk the each sandwich into the egg mixture {make sure to flip so both sides are coated, allowing excess liquid to drip off. Immediately place onto cookie crumbs and dredge each side, pressing lightly to adhere the crumbs to the outside of the bread. Repeat with second sandwich.
Place each piece in skillet. Cook about 3-4 minutes on each side until they're golden and have a bit of a crunch.*
Serve warm with powdered sugar and extra strawberries if desired.