With a little oil, grease the bottom and sides of a 9-inch by 13-inch rimmed sheet pan.
Combine the water, flour, salt, and pepper in a medium pot. Whisk together until smooth, and there are no lumps. Place over medium-low heat, and cooking, stirring constantly, until the mixture thickens up like polenta, about 10 minutes.
Spread the panelle “batter” into the prepared pan, and use an oiled rubber spatula to smooth into an even thin layer. Let cool at room temperature until firm, about 1 hour.
Once cooled and firm, cut into desired shape. My preferred is either 3-inch (TK-cm) squares, or 2-inch by 3-unch rectangles.
Add ½ inch of oil to a shallow skillet. Heat until shimmering. Add a few of the panelle, and cook until golden underneath, 2 to 3 minutes. Flip, and cook until golden on the other side, 2 to 3 minutes more. This needs to be done in batches to avoid crowding the pan, so they brown nicely.
Serve hot with marinara sauce, or as we grew up eating them in Brooklyn, tucked between a roll with ricotta cheese and grated pecorino.
Make Ahead Tip: Once cooled and cut, the panelle can be frozen until ready to fry and eat. Line a sheet pan with parchment paper. Arrange the panelle pieces in a single layer. Freeze until firm, then transfer to a ziptop bag. Fry panelle according to directions above directly from the freezer, no need to thaw in advance.