Place the potatoes in a large pot of salted water. Bring to a boil and cook until fork-tender, 12 minutes. In the last 5 minutes of cooking, stir in the coleslaw; drain and return to the pot. Stir in 1/2 cup sour cream and 1/4 cup broth; season with salt and pepper. Smash with a potato masher.
Meanwhile, coat the pork with the flour and season with salt and pepper. In a skillet, heat 1 tbsp. EVOO over medium-high heat. Add the pork and cook, turning once, until browned, 5 minutes. Cover, lower the heat to medium-low and cook for 5 minutes. Transfer to a plate and keep warm.
In the same skillet, heat the remaining 1 tbsp. EVOO over medium-high heat. Add the onion and mushrooms and cook until lightly browned, 5 minutes. Add the remaining 3/4 cup broth, increase the heat to high and cook, stirring, for 5 minutes. Stir in the remaining 1/2 cup sour cream; season with salt and pepper. Spoon on top of the pork chops and serve with the potatoes.