Mix garlic, ginger, umeboshi, lime juice, and zest in a bowl.
Whisk in the oil and stir in the herbs to complete the dressing.
Preheat the grill to a high temperature.
Marinate monkfish cheeks in half of the dressing for 30 minutes in a shallow dish.
Blanch asparagus in boiling water for one minute, then cool in cold water and drain.
Coat lettuce, avocado, and asparagus with olive oil and salt.
Grill the vegetables until charred on each side and set aside at room temperature.
Grill the monkfish cheeks for 2 to 3 minutes per side.
Toss the cooked monkfish in the marinade and rest for 3 minutes.
Cut charred vegetables into bite-sized pieces and toss with edamame and mint.
Arrange vegetables on a platter, top with monkfish cheeks, and drizzle with remaining dressing.