Heat olive oil in a large skillet over medium heat. Season the salmon fillets with salt and pepper, then add them to the skillet, skin-side down. Cook for about 4-5 minutes until the skin is crispy, then flip and cook for an additional 3-4 minutes. Remove the salmon from the skillet and set aside.
In the same skillet, add the minced garlic and sauté for about 30 seconds until fragrant. Be careful not to burn it.
Stir in the orzo and cook for 1-2 minutes, allowing it to toast slightly.
Pour in the broth, then add the cherry tomatoes, lemon juice, lemon zest, and dried oregano. Bring to a boil, then reduce the heat to a simmer. Cover and cook for about 10-12 minutes, stirring occasionally, until the orzo is tender and the liquid is mostly absorbed.
Stir in the spinach and return the salmon to the skillet, nestling it into the orzo. Cover and cook for an additional 2-3 minutes until the spinach is wilted and the salmon is heated through.
Remove from heat and garnish with fresh parsley. Serve with lemon wedges on the side.