For the spice rubbed lamb chops hoisin: Combine the anise, ginger, coriander, garlic powder and chile de arbol in a bowl. Rub the spice mix onto the lamb chops.
Heat a charcoal grill for direct heat or a gas grill for high heat. Brush the lamb with canola oil and sprinkle with salt and pepper. Grill the lamb until slightly charred on all sides and cooked to medium-rare, about 8 minutes total. Brush the lamb with the hoisin just before removing from the grill.
For the grilled bok choy salad: Brush the bok choy with canola oil and sprinkle with salt and pepper. Grill the bok choy, cut-side down for about 4 minutes; flip, and grill another few minutes until the stems are crisp-tender. Chop the bok choy coarsely and put in a bowl.
For the vinaigrette: Whisk the fish sauce, vinegar, lime juice, chile sauce and soy sauce and sprinkle with salt and pepper in a bowl. Whisk in the canola and sesame oil. Toss the vinaigrette with the grilled bok choy salad; taste and season with salt and pepper.
Place the lamb on a platter and scatter with the cilantro and mint over the top. Serve with the grilled bok choy salad.