Preheat the oven to 350 degrees F. Line a buttered 15 by 10 (1-inch) jelly roll pan with parchment paper. Butter the paper, dust with flour, and tap out the excess.
Melt the butter in a small saucepan over medium-high heat. Add the flour and cook, stirring, for 3 minutes. Increase the heat to high, whisk in the milk, and bring to a boil. Reduce the heat to medium and simmer for 5 minutes. Transfer to a large bowl and whisk in the egg yolks 1 at a time. Season with the salt and pepper. Beat the egg whites until soft peaks form. Stir 1/3 of the whites into the yolk mixture and fold in the rest. Pour the batter into the bottom of the prepared pan and smooth gently with a metal spatula. Transfer to the oven and cook until golden and firm to the touch, about 15 minutes.
Increase the oven heat to 375 degrees F. Cover the egg sponge with a buttered piece of parchment paper, buttered side down. Cover with a damp kitchen towel and invert onto a work surface. Peel off the paper from the top.
Sprinkle the cheese over the sponge, leaving a 1/2-inch border on all sides. Arrange the ham and pepper strips on top and sprinkle on the parsley. Place a flat baking sheet next to the sponge. Starting with 1 of the longer sides, use the towel to help roll the sponge up jelly roll fashion. Carefully roll onto the baking sheet pan. Return the roulade to the upper third of the oven and bake until the cheese has melted, 8 to 10 minutes. Use a serrated knife to cut crosswise into 1/2-inch-thick slices.