Preheat the oven to 400 degrees F. Line a baking sheet with parchment.
Melt the butter in a small saucepan over medium heat. Stir in the garlic and crushed red pepper flakes, and cook until fragrant, about 2 minutes. Pour in the wine and reduce until the alcohol smell is no longer present and the sauce is a nice golden color, 4 to 5 minutes. Remove the pan from the heat and stir in the shrimp, lemon zest and parsley; sprinkle with salt and pepper and set aside.
Roll out the dough into a 20-by-14-inch rectangle on a lightly floured work surface. Working from the shorter end of the dough, distribute the mozzarella over half of the dough, leaving a 1-inch border on the sides. Evenly distribute the shrimp and sauce over the cheese. Working from the shorter end, tightly roll the dough up, jelly roll-style, into a log. Pinch the open seams together to seal, then tuck them underneath the log.
Transfer the log to the prepared baking sheet, and brush with the beaten egg. Bake until the bread is golden brown and the shrimp are cooked through, 40 to 45 minutes. (The filling may leak out on the side.)
Let the bread cool for at least 10 minutes. Transfer to a cutting board. Halve the bread lengthwise, cut each half crosswise into 4 equal pieces and serve warm.
To make rolling and shaping the dough easy, keep the dough refrigerated until 10 to 15 minutes before you are ready to use it.
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