Put the potatoes in a medium saucepan and cover with cold water by 1 inch; season with salt. Bring to a boil, then reduce the heat to medium and simmer until tender, about 9 minutes, adding the asparagus during the last 2 minutes of cooking. Drain.
Meanwhile, combine the breadcrumbs and 1 tablespoon tarragon in a shallow dish. Season the pork with 1/2 teaspoon salt, a few grinds of pepper and the paprika. Spread 1 tablespoon mustard on one side of the chops, then press, mustard-side down, into the crumb mixture.
Heat the vegetable oil in a large nonstick skillet over medium heat. Add the pork chops, crumb-side down, and cook until golden brown and just cooked through, about 4 minutes per side.
Whisk the sour cream, vinegar and the remaining 1 tablespoon each mustard and tarragon in a large bowl. Add the potatoes and asparagus, the basil, 1/4 teaspoon salt and a few grinds of pepper; toss. Serve with the pork chops.