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Preheat grill to medium high heat. Place medallions on the grill and cook 3-4 minutes per side. While pork cooks, prepare garlic mayonnaise by adding garlic to the mayo and stirring well.
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Once pork is finished, set aside and let rest. Put buns on the grill and toast until golden brown.
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Once pork has rested, slice into strips.
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To assemble sandwiches, smear buns with garlic mayonnaise, then pieces of pork, bbq sauce, 2 slices of cheddar cheese, red onion, and then top with arugula.
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Serve immediately.