In a bowl, sprinkle the shrimp with the 1 tablespoon salt and toss to coat evenly. Let stand for no more than 1 minute, then rinse well and drain. Pat the shrimp dry.
In a large frying pan over medium heat, warm the olive oil. When the oil shimmers, add the shrimp and cook until bright orange on one side, about 2 minutes. Turn with tongs and continue cooking until the shrimp are opaque throughout, 1 to 3 minutes more.
Add the garlic, parsley and lemon zest and cook until fragrant but not browned, about 30 seconds. Add the lemon juice and bring to a boil, scraping up the browned bits from the pan bottom. Cook until the liquid is nearly evaporated, then remove from the heat and add the butter. Stir quickly and constantly as the butter melts. Adjust the seasonings with salt and pepper. Add shrimp stock to thin sauce, as needed
Adapted from Williams-Sonoma Fish for Dinner (Weldon Owen, 2009)