Place the cubed potatoes in a medium saucepan and cover with water. Add a pinch of salt and bring to a boil. Cook for 15 minutes or until the potatoes are fork tender.
While the potatoes cook, mix the soy sauce, honey, and minced garlic in a small bowl. Set the mixture aside.
Heat the vegetable oil in a large skillet over medium high heat. Season the pork chops with salt and pepper on both sides. Add them to the skillet and cook for 4 to 5 minutes per side until browned and cooked through. Remove the chops to a plate.
Add the green beans to the same skillet. Cook for 4 minutes, stirring often, until they start to soften. Pour in the soy honey mixture and return the pork chops to the skillet. Simmer everything together for 2 minutes so the sauce thickens slightly and coats the chops and beans.
Drain the potatoes and return them to the saucepan. Add the milk and butter. Mash until smooth. Season with salt and pepper to taste.
Serve the pork chops with the green beans and sauce spooned over the top alongside the mashed potatoes.