Preheat broiler with a rack set about 6 inches from heat source.

Whisk together cane syrup, cider, and mustards; bring to a low simmer and cook 5 minutes; keep warm. Melt butter in oil in a skillet over medium-high heat. Add ham and fry, turning once, until well browned. Brush generously with glaze and broil until glaze is browned and bubbly; turn ham over and repeat. Serve hot.