Position a rack in the center of the oven and preheat to 350 degrees F.
Line a 15-by-18-inch sheet pan with parchment paper leaving a 2-inch overhang on each of the two narrow ends. Brush with melted butter. Whisk the eggs, cream, cheese and salt in a large bowl. Pour into the prepared pan and bake until the eggs are puffed on the edges and just set, 20 to 25 minutes.
Imagine the omelet is divided into three equal sections running lengthwise. Top one section with a layer of the spinach, another with the prosciutto and the last with the peppers; leave a little space between each section. Cover with foil and let sit 10 minutes to allow the spinach to wilt and the toppings to warm.
Remove the foil and, using the parchment for handles, carefully transfer the omelet to a cutting board. Starting at one of the short ends, lift the parchment up and use it to help tightly roll up the omelet, pulling the parchment back as you go so it does not get caught in the roll. Using a sharp chef's knife, cut the omelet into slices and arrange on a platter.
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