Slice it thin.
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Remember in 'Goodfellas' when Paulie used a razor blade to shave garlic so thin, it peeled off the clove? In an ideal world, Chuck Kelsey of Cutty's would have Paulie on deli detail. Kelsey says that "if you're using fatty meat, like salami, you should slice it so thin it'll fold over on itself easily. That way, the fat melts as soon as it hits your tongue. You get all of the flavor without having to bite through the wall of meat." The same goes for cheese, Kelsey says, or even vegetables. Use a mandolin or peeler to shave veggies like radishes, fennel, carrots, and onions nice and thin. You'll still get their fresh crispness, but you'll bite through everything easily, and nothing will jump out of the sandwich.