Bring a large pot of cold water to a boil over high heat and salt it generously. Add the spaghetti and boil, stirring occasionally, until al dente. Drain.
Meanwhile, melt the butter in a large Dutch oven or deep stove-top casserole dish over medium heat. Scatter the flour over the butter and mix with a wooden spoon into a paste. Continue stirring in a figure "8", making sure to get into the corners of the pan, until the paste puffs slightly and lightens in color, about 1 minute. Off the heat gradually whisk the milk into the paste. Return to medium-high heat and whisk until thickened, then simmer, stirring occasionally until the sauce has the consistency of heavy cream, about 8 to 10 minutes. Whisk in the cream cheese, Worcestershire sauce, and nutmeg. Season with salt, pepper.
Reduce heat to low and whisk 1 cup Monterey Jack. Stir in the broccoli, peas, pepperoni and spaghetti, and heat until warmed through.
Top casserole with the remaining 1 cup cheese; transfer to the broiler, and cook casserole until brown and bubbly. Cool slightly and serve.
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