When chef Jason Cheek opened Southern Proper this year, he sought to bring a taste of his native North Carolina to Boston. Step inside the South End restaurant, and you’ll see he’s done just that: The eatery takes design cues from Cheek’s grandmother’s living room, serving up comfort food on mismatched plates. The kitchen, meanwhile, cranks out platters of tender fried chicken, not to mention flaky popovers and out-of-this-world homemade pickles.