Combine oils, honey, ginger, garlic, five spice, rice vinegar, soya sauce and sesame seeds in a bowl.
Mix half the marinade with steaks and the other half with bok choy and mushrooms.
Grill steaks over direct medium-high heat for about 10 minutes until a digital thermometer probe reads 170F (77C).
Remove from grill, cover loosely with foil and let stand for 10-15 minutes before serving.
Grill vegetables over direct medium-high heat for about 4 minutes per side. Extra vegetable marinade can be drizzled over vegetables and steaks during cooking.
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