Season pork roast with kosher salt and 1 1/2 teaspoons pepper.
Process gingersnap cookies in a food processor to fine crumbs. Transfer crumbs to a plate or shallow bowl. Roll roast in crumbs to coat.
Heat olive oil in a large oven-proof skillet over medium-high heat. Cook roast in hot oil until all sides are browned, 8 to 10 minutes. Transfer skillet with roast to the center rack of the oven.
Roast pork in the preheated oven until it is slightly pink in the center, 15 to 20 minutes. An instant-read thermometer inserted into the center should read at least 145 degrees F (63 degrees C). Remove roast to a serving platter and cover with foil.
Pour apple cider and chicken stock into the same skillet used to cook the pork roast and bring liquid to a boil while scraping the browned bits of food off of the bottom of the pan with a wooden spoon. Add apple slices and currants; simmer until sauce reduces to 1/2 cup, 5 to 10 minutes. Stir butter into apple mixture until butter is completely melted and incorporated, about 1 minute more. Season sauce with salt and pepper to taste.
Slice pork roast into 1/2-inch thick slices and pour apple currant sauce over the top.