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1
Make the marinade by whisking together the garlic, salt, red pepper flakes, Worcestershire sauce, mustard, vinegar and oil. Place the mushroom caps in a large zip-topped bag and pour marinade over them. Seal and refrigerate for at least an hour or up to overnight, flipping the bag periodically.
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2
Make the arugula mayo by combining the tofu, vinegar, mustard, lemon juice, Worcestershire sauce, salt, pepper, olive oil, arugula and cheese in the bowl of a food processor. Puree until the mixture is smooth and bright green. Refrigerate until just before serving the burgers. You can make it ahead--it will keep for three days.
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3
Preheat the oven to 400u00b0F. Arrange the slices of prosciutto on a silpat or parchment lined baking sheet, and bake 2 to 3 minutes before flipping, then a minute or two on the other side. The time will vary according to your oven, but the slices should darken in color and become slightly crisp (they'll crisp up nicely as they cool). Watch them carefully, they burn easily. Set aside while you cook the mushrooms.
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4
Adjust the top oven rack so it's four inches below the heating element, and preheat the broiler. Remove the mushrooms from their marinade, brushing off and discarding excess, and place them on an oiled baking rack set inside a rimmed baking pan. Broil for 2 to 3 minutes per side. Toast your hamburger buns.
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5
To assemble the burgers, spread some arugula mayo on the bottom of the bun, top with a mushroom, 2 pieces of prosciutto, and additional arugula mayo if you like. I like to serve burgers with roasted potato wedges.
