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Preheat oven to 400
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Toss asparagus with olive oil and salt and pepper to taste on a baking sheet
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Roast asparagus 5-6 minutes, depending on size (you don't want it completely soft because it will be broiled in the tartine), set aside
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Mix equal amounts of mayo and Dijon together
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Cut bread into thirds and slice pieces in half lengthwise
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Increase oven to broil, place bread pieces on baking sheet and broil 2 minutes
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Spread mayo/Dijon mixture on bread
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Put 2-3 asparagus spears on each piece of bread, top with a few pieces of ham and a bit of shredded cheese
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Broil tartines 8-10 minutes
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Toss some arugula on top of each