In a large bowl, toss the shrimp with 3 tablespoons olive oil, the lemon juice and zest, 4 minced garlic cloves, crushed red pepper flakes, and a generous pinch of kosher salt and pepper; let sit for 10 minutes.
Heat 2 tablespoons unsalted butter in a large skillet over medium heat until melted.
Add the orzo to the melted butter and cook, stirring often, until the orzo is lightly golden and toasty, about 3–4 minutes.
Stir in 2 minced garlic cloves and cook for 30 seconds, then pour in 2 1/4 cups chicken stock and bring to a boil.
Reduce heat to a simmer, cover, and cook until the orzo has absorbed most of the liquid and is tender and fluffy, about 12–15 minutes.
Add the marinated shrimp to the cooked orzo, stir to combine, cover, and cook until the shrimp are pink and opaque, about 5–8 minutes.
Remove from heat, stir in chopped parsley and a spritz of lemon; if desired, stir in 1–2 tablespoons additional melted butter before serving. Serve immediately.