Season salmon with salt and pepper.
In a large, deep sided skillet over medium heat, heat oil. Add salmon, skin side down and cook until salmon flakes easily with a fork or internal temperature reaches 140°, about 6 minutes per side. Remove salmon from skillet.
Add shallot and cook until soft, 5 minutes, then add garlic and cook until fragrant, 1 minute more. Add orzo and cook, stirring, 1 minute. Add vinegar and stir until evaporated. Add broth and scrape any brown bits from bottom of pan. Season with oregano, red pepper flakes, salt, and pepper. Bring to a simmer, then reduce heat and cook, covered, until orzo is tender 6 to 8 minutes. Lift lid and stir occasionally to ensure orzo isn’t sticking to the bottom of the pan.
Stir in spinach, tomatoes, feta, and herbs. Return salmon to skillet.
Serve with lemon wedges.
