In a long shallow dish, whisk together the eggs, milk, granulated sugar, vanilla extract, and cinnamon until smooth; set the batter aside.
Heat a large nonstick skillet over medium-high heat, then reduce to medium and lightly grease with butter.
Working one flatbread at a time, submerge it in the batter briefly, allow excess to drip off, and place in the hot skillet.
Cook each flatbread 45–60 seconds per side, until golden, then transfer to a plate and repeat with remaining flatbreads (there will be leftover batter).
If serving plain, roll each flatbread and serve with syrup. To make strawberries and cream: spread about 2 heaping tablespoons softened cream cheese over the top of each cooked flatbread.
Evenly layer thinly sliced strawberries on top of the cream cheese, sprinkle the strawberries with about 1 teaspoon powdered sugar, then roll each flatbread up tightly.
Serve whole as roll ups or slice into 1/2-inch slices to make pinwheels; secure pinwheels with toothpicks if desired and dust with additional powdered sugar. Serve with syrup.