
In a measuring cup, whisk together the butter, soy sauce, lemon zest, lemon juice, honey, pepper, and garlic.
In a large bowl, combine the mushrooms, salt, and half of the butter mixture, tossing to coat well. Cover and marinate at room temperature for 30 minutes. Reserve the remaining butter mixture.
Preheat the grill to medium-high heat (400°F to 425°F).
Thread the mushrooms and green onions in an alternating pattern on 6 (12-inch) skewers.
Grill the skewers, covered, until grill marks form on the mushrooms, about 3 minutes. Turn the skewers and continue grilling until grill marks form on the other side, 3 to 4 minutes more. Uncover the grill and brush the mushrooms and green onions with some of the reserved butter mixture. Grill, uncovered, turning the skewers occasionally, until the mushrooms are well browned and tender, 1 to 2 minutes more.
Remove the skewers to a serving plate and brush with more of the butter mixture. Sprinkle with the thyme before serving.