Wrap artichoke hearts in paper towels; squeeze out liquid and coarsely chop. Set sandwich wraps on work surface. Lay 4 cheese slices down center of each, leaving a 1-inch border at top and bottom. Dividing evenly between wraps, layer artichoke pieces, bell pepper, and spinach on top of cheese. Season with salt and pepper.
Fold in tops and bottoms of wraps by about 1 inch, then roll tightly from one of the open sides to enclose filling.Wrap tightly in plastic or waxed paper. Refrigerate until ready to serve, up to overnight.