Pat the shrimp very dry with paper towels. Season with 1/2 teaspoon kosher salt and all of the black pepper. Stir together the garlic, Aleppo pepper, lemon zest, and parsley in a small bowl; set near the stove.
Set a large skillet over medium-high heat and add 2 tablespoons butter. When the butter foams, add half the shrimp in a single layer and sear 45–60 seconds per side, just until lightly golden at the edges. Transfer to a plate and repeat with the remaining shrimp (add a small pat of butter only if the pan looks dry).
Reduce heat to medium. Add the garlic–Aleppo mixture to the skillet and stir for 30–45 seconds until fragrant, scraping up any browned bits so the garlic doesn’t scorch.
Pour in the white wine and lemon juice. Simmer at a brisk bubble for 2–3 minutes, scraping the pan, until the liquid is reduced by about half.
Return the shrimp and any collected juices to the skillet and toss for 30–60 seconds, just until the shrimp are opaque and cooked through. Remove the pan from the heat.
Off the heat, whisk in the remaining 4 tablespoons cold butter, one piece at a time, to create a glossy emulsion. Stir in the parsley and a pinch of the remaining salt (taste and add more salt if needed). Let the sauce stand 1 minute to thicken slightly.
Serve immediately, spooning plenty of the garlic-butter sauce over the shrimp. Finish with an extra sprinkle of parsley or lemon zest if you like.