Butterfly and clean the shrimp. Preheat an oven to 450°F. Use a small, sharp knife to slice along the back of the shrimp, starting from the head end and cutting toward the tail, being careful not to cut all the way through. Gently open the shrimp like a book, then remove the dark vein with the tip of the knife. Repeat until all shrimp are butterflied, then toss with 1 Tbsp extra virgin olive oil and ½ tsp kosher salt.
Make the breading. Melt 2 Tbsp (28g) butter over medium heat in a small nonstick skillet, then add 2 chopped garlic cloves. Cook until fragrant, about 1-2 minutes. Add ⅔ cup (70g) breadcrumbs, then cook, stirring often, until they turn golden brown, another 1-2 minutes. Transfer to a bowl or shallow dish then stir in ⅓ cup (35g) Parmigiano Reggiano cheese, 2 tsp lemon zest, 2 tsp dried oregano, ½ tsp kosher salt, and ¼ tsp crushed red pepper flakes. Stir well.
Assemble. Coat the bottom of a baking dish with a tablespoon or two of olive oil. Arrange the shrimp in the dish, butterflied side down, tails pointing up. Generously spoon the breadcrumb mixture on top of the shrimp, leaving the tails uncoated.
Roast the shrimp. Pour ¼ cup (60ml) of white wine around the skillet, then drizzle the shrimp with the remaining tablespoon of olive oil. Transfer to the preheated oven and cook for 10-12 minutes, until light golden brown. Set the broiler to high, then place the shrimp underneath and cook for an additional 2 minutes until you achieve a golden crust.
Garnish, then serve. Sprinkle with chopped parsley and a pinch of flaky sea salt, then serve hot with lemon wedges.