Bring a large pan to medium high heat and add vegetable oil to lightly coat the pan (~ 1 Tbsp).
Sear the pork chops on both sides ~ 3 minutes or until the pork has a nice brown color.
Take pork out and set aside on a plate. The pork is not done yet so don't eat it!
Reduce heat and add ~1 Tbsp olive oil and shallots to pan, cook for ~ 3-4 minutes or until soft and translucent. Add more olive oil if needed.
Add garlic and ginger. Cook for an additional 1-2 minutes or until fragrant. Add more olive oil if the pan is dry.
Add peaches, sherry, and tomato sauce. Bring to a boil, and simmer covered ~ 5 minutes.
Add pork chops (and any resting juices) gently nuzzling into the peach sauce. Cover and cook an additional 3-5 minutes or until pork is cooked through or registers 145F.
Taste the sauce. Add more olive oil (I love a glossy sheen of oil on the sauce) to taste and salt to taste.
Plate tomato and peach sauce and add the seared pork on top of it.
Notes
Wanna see your beautiful pork chop sear? Plate the peach and tomato sauce first and lay the pork on top for a prettier presentation.
Peel the peaches if you want a smoother peach sauce. Leave the skin on if you don't mind a little rustic texture.