Add 3 tbsp olive oil to a large high-sided skillet or frying pan and turn to medium heat. Once the pan is hot, add the shrimp and 1 tsp salt. Cook 3-6 minutes or until the shrimp are cooked through / pink. Transfer the shrimp to a plate or bowl and set aside.
Keep the pan on medium heat and add the diced onion, cook until softened, about 3-4 minutes.
Add in the minced garlic, ½ tsp salt, dried oregano and ground pepper. Cook until fragrant, about 1-2 minutes.
Stir in the orzo and lemon zest until well combined with ingredients in the pan.
Stir in the vegetable broth and bring to a simmer. Once simmering, keep at a simmer over medium-low heat until most of the liquid is absorbed and the orzo is al dente, about 10-12 minutes, stir occasionally to make sure the orzo doesn’t stick to the bottom of the pan. If you have a lid for the skillet, keep it on the pan most of the way while the orzo cooks, removing the lid to stir.
Once the orzo is cooked, add the shrimp back to the pan and ¼ cup pesto, stirring to combine and cook on low for another 1-2 minutes. Taste and adjust seasoning with 1/4 cup more pesto if desired.
Remove from the heat and serve immediately, garnished with fresh basil leaves, squeeze of lemon juice and/or a pinch of red pepper flakes.