Heat the oil in a large skillet with a tight-fitting over medium heat.
Add garlic, gingerroot, lime zest and leeks; cook and stir for 2 to 3 minutes or just until onion is becoming translucent. Add next 8 ingredients (pork cutlets through black pepper), stirring gently.
Reduce heat, cover and simmer for 10 to 20 minutes or until cutlets are done (or just slightly pink in the centers), turning once half way through cooking time.
Stir in spinach until wilted.