Bring a large pot of generously salted water to a boil over high heat. Add the broccolini and cook until fork-tender, about 3 minutes. Using a slotted spoon, transfer the broccolini to a plate, reserving the cooking water. When cool enough to handle, chop into 1-inch (2.5-cm) pieces. Set aside. 

Return the pot of water to high heat and bring to a boil. Add the orzo and cook until al dente, about 2 minutes less than the package directions for doneness. Drain well and set aside. 

In a small pan over low heat, warm the broth. Keep warm while you cook the shrimp. 

In a large frying pan over medium-high heat, melt the butter in the olive oil. Add the garlic and sauté just until soft, about 1 minute. Add the shrimp and season well with salt and pepper. Cook, flipping once, until the shrimp are bright pink, about 5 minutes total. Using a slotted spoon, transfer the shrimp to a clean plate and set aside. 

Reduce the heat to medium-low and stir in the orzo and½ cup (4 fl oz/125 ml) of the warm broth, scraping up any browned bits on the bottom of the pan. Cook gently, stirring often, until the broth is absorbed, about 2 minutes. Repeat to add the remaining broth ½ cup at a time, allowing the liquid to be absorbed before adding more. Stir in the cheese, parsley, shrimp, and broccolini. Season with salt and pepper and serve right away.