In a medium bowl, stir together shrimp, 1 tsp olive oil, lemon zest, red-pepper flakes, ¼ teaspoon salt, ¼ teaspoon pepper and half of the garlic. Set aside to marinate. (This step can be done up to 1 hour in advance.)
Add butter and 1 tsp olive oil to a medium skillet set over medium heat. When the butter starts to bubble, add the orzo and ½ teaspoon salt and cook, stirring often, until the orzo is toasted, about 3 minutes. Add the garlic and cook for 1 more minute.
Carefully add the wine to the orzo — it will bubble — and stir until absorbed, about 1 minute. Stir in broth, reduce heat to low, cover, and cook until orzo is al dente, about 9-10 minutes.
Add the shrimp in an even layer on top of the orzo, cover, and cook until all the shrimp is pink and cooked through, 2 to 4 minutes. Remove from heat and let sit, covered, 2 minutes.
Mix in lemon juice to taste. Season with extra salt and pepper to taste. Sprinkle with parsley or chives. Serve with extra lemon wedges on the side.