Wilt spinach in a pan with olive oil and garlic for 2 minutes. Squeeze out all excess moisture — watery filling will steam the chicken from inside and prevent browning.
Mix wilted spinach with cream cheese and a pinch of salt until combined.
Make a pocket in each chicken breast: hold the breast flat and insert a sharp knife into the thick side, cutting three-quarters of the way through without slicing all the way.
Stuff each breast generously with the spinach mixture. Press closed and secure with 1–2 toothpicks.
Season outside with salt, paprika, and a drizzle of olive oil.
Sear in an oven-safe skillet over medium-high heat, 3 minutes per side until golden.
Transfer to oven and bake 15–18 minutes until internal temperature reaches 165°F.