Heat the broth in the microwave or in a saucepan over low heat just until steamy.
Place a large sauté pan or skillet over medium low heat and melt in the butter. Add in the shallot, season with salt and pepper, and cook, stirring frequently for 1 to 2 minutes. Add in the garlic and turmeric and cook for 30 seconds. Turn the heat up to medium, add in the orzo, and cook for 1 to 2 minutes to lightly toast the pasta.
Add in the white wine and simmer until fully absorbed. Add about a ½ cup of the hot broth into the orzo and stir frequently until the broth is absorbed before adding in another ½ cup. Continue adding broth in this manner until the orzo is cooked to al dente. This should take approximately 20 minutes and use anywhere from 4 ½ to 5 cups of broth.
When the rice is just cooked, stir in the spinach and shrimp, cover the pan with a lid, and cook just until the shrimp are pink and opaque, about 3 to 4 minutes. Just before serving, stir in the lemon zest, lemon juice, herbs, red pepper flakes, and season with salt and pepper, if needed.