Heat olive oil in a deep skillet over medium heat. Add garlic and Italian seasoning; sauté just until fragrant, 30 to 60 seconds.
Add orzo and stir to toast lightly, about 30 seconds. Pour in broth, add salt and pepper, and bring to a gentle boil.
Reduce heat to medium-low and simmer, stirring occasionally, until the orzo is nearly tender and most of the liquid is absorbed, 7 to 9 minutes.
Nestle shrimp into the orzo. Scatter spinach over the top. Add lemon zest and lemon juice. Cover and cook shrimp just until pink and opaque, turning once, 2 to 3 minutes per side.
Turn off heat. Stir in Parmesan cheese. Adjust seasoning to taste.
