Fried Artichoke Sandwiches

Name: Fried Artichoke Sandwiches
Ingredients: 1 12-ounce package frozen quartered artichoke hearts, thawed; 1/3 cup all-purpose flour; Kosher salt and freshly ground pepper; 2 large eggs; 1/2 to 2/3 cup vegetable oil, for shallow frying; 1/3 cup mayonnaise; 1/3 cup sliced pepperoncini, plus 1 tablespoon brine; 4 small ciabatta rolls, split and toasted; 1/4 cup shredded Parmesan cheese; 1 cup thinly sliced romaine hearts (about 3 leaves); 1 cup thinly sliced radicchio (about 1/4 head); Potato chips, for serving