Whisk together the olive oil, vinegar, shallots, thyme, salt, and pepper. Thread the mushrooms on thin metal or soaked wood skewers and arrange on a baking sheet. Brush with the olive oil mixture and grill over moderately hot coals on both sides until tender and golden brown. Remove mushrooms from skewers and quarter or slice thickly.
Toss greens and mushrooms pecan vinaigrette and arrange on plates with pears, toasted pecans and sprouts. Serve immediately.
Whisk the oil, grapefruit juice and sugar together until sugar is dissolved. Stir in mint and add drops of hot sauce and salt and pepper to taste. Let sit for at least 30 minutes for the flavors to develop.