1.In a small saucepan, stir together balsamic vinegar and honey and bring to a boil over high heat. Reduce heat to low and allow mixture to simmer, stirring frequently, until thickened, about 2 minutes. Set aside to cool while making stuffed mushrooms.
2.Place an oven rack in upper third of oven and turn on oven broiler.
3.In a medium bowl fold together tomatoes, red onion, 2 tablespoons basil, and a good pinch of salt and pepper. Set aside.
4.Brush each mushroom cap on all sides with Serious Garlic Butter and place hollow side up on a rimmed baking tray. Broil until just beginning to soften, about 5 minutes.
5.Fill hollows of mushrooms with tomato mixture and sprinkle with pecorino cheese.
6.Garnish with a drizzle of cooled balsamic glaze, remaining 1 tablespoon basil, and some Lemon Tarragon Cashews. Enjoy immediately.