Make the breadcrumbs: In a large stainless-steel skillet, heat the butter over medium heat until melted and slightly browned but not burned. Add the breadcrumbs. Using a wooden spoon, stir the breadcrumbs to coat with the brown butter and toast until golden brown, 2 to 3 minutes. Remove from the heat. Stir in the chopped chives and oregano and the lemon zest. Season with salt and pepper to taste, pour into a small bowl and set aside.
Make the pasta: Bring a large pot of generously salted water to a boil. Wipe out the skillet, add the olive oil and heat over high heat until shimmering. Season the shrimp all over with salt and pepper. Working in two batches, add the shrimp to the pan in one layer and cook for 1 minute. Turn and cook 1 more minute. Using a slotted spoon, transfer the shrimp to a large bowl.
Add the garlic and shallot to the pan and cook for 1 minute. Add a touch more oil if the pan is dry. Add the wine, lemon juice, red pepper flakes and dried oregano and simmer for 3 minutes. Whisk in the butter piece by piece, thoroughly incorporating each piece before adding the next. Taste and season with additional salt and pepper as needed. Add the shrimp back to the pan and simmer until completely cooked through, about 2 minutes. Stir in the parsley. Remove the skillet from the heat.
Meanwhile, add the pasta to the boiling water and cook until just tender, about 10 minutes. Reserve 1 cup of the cooking water and drain the pasta in a colander. Add to the skillet with the shrimp, add the parsley and toss, adding some of the cooking water if necessary to keep it moist. Transfer to bowls and top with some of the herbed breadcrumbs.