Add the shrimp to a bowl with 1 grated garlic clove, a generous pinch of salt and pepper, and a drizzle of olive oil. Toss together and let marinate while preparing the remaining ingredients.
Heat a large skillet or Dutch oven over medium-high heat with the olive oil. Sear the shrimp for 1–2 minutes per side until pink and lightly golden. Transfer to a plate.
Lower the heat to medium. Add the shallot to the same pan with a pinch of salt and cook until softened. Stir in the remaining grated garlic and cook until fragrant.
Pour in the juice of 1 lemon and scrape up any browned bits from the bottom of the pan. Season lightly with salt and pepper.
Add the orzo and stir for about 1 minute so it coats in the lemony mixture.
Pour in the chicken bone broth and bring to a gentle simmer. Cook uncovered, stirring occasionally, until the orzo is tender and creamy and most of the liquid has absorbed.
Stir in the butter, lemon zest, fresh dill, and some of the feta. Taste and season with additional salt and pepper as needed.
Add the shrimp back into the pan and gently fold everything together.
Top with extra feta, fresh dill, black pepper, and additional lemon zest before serving.