Marinate the shrimp. In a bowl, toss the shrimp with 1 tablespoon olive oil, 1 teaspoon lemon zest, a pinch or two of red pepper flakes, ½ teaspoon sea salt, freshly ground pepper, and 1 minced garlic clove. Set aside. (You can do this up to 1 hour ahead; keep it in the fridge.)
Toast and cook the orzo. Melt 2 tablespoons butter in a medium saucepan over medium heat. When it bubbles, add the orzo and stir often until lightly toasted, about 2 minutes. Stir in the stock, reduce the heat to low, cover, and cook until al dente, about 12 minutes.
Sear the shrimp. While the orzo cooks, heat a 12-inch skillet over medium heat. Add half the shrimp in one layer and cook undisturbed until they start turning pink, about 1 minute. Flip, cook 1 minute more, and transfer to a plate. Repeat with the rest. They'll finish cooking in the sauce.
Make the brown butter sauce. In the same skillet, melt the remaining 5 tablespoons butter over medium heat. Cook, swirling the pan, until it foams, turns golden brown, and smells nutty, 2 to 3 minutes. Add the shallot and remaining garlic and sauté until fragrant, about 1 minute. Add the wine, lemon juice, remaining zest, a pinch of red pepper flakes, and plenty of black pepper. Simmer until the sauce reduces by about half, 4 to 5 minutes.
Finish the shrimp. Return the shrimp and any juices to the skillet and simmer just until the flesh is pearly and opaque throughout (145°F/63°C), 1 to 2 minutes. Taste and adjust the salt.
Serve. Spoon the orzo into shallow bowls, top with the shrimp, and pour the sauce generously over everything. Finish with parsley and more lemon if you like. Serve right away, with crusty bread.