For marinade, whisk all ingredients in a small bowl until blended.
For tacos, place mushroom caps in a large food-safe resealable plastic bag. Add marinade; seal bag and turn several times to coat mushrooms evenly. Marinate at room temperature 10 to 15 minutes.
Preheat grill to high. Brush chiles with oil. Season lightly with salt and pepper. Grill chiles, turning once, until just tender and starting to blister, about 7 minutes. Cool slightly. Cut into 1/4-inch-thick strips.
Reduce grill setting to medium-high. Remove mushrooms from marinade; discard marinade. Grill mushrooms on lightly oiled grill grid, turning once, until tender, about 10 minutes. Cool slightly. Cut into 1/4-inch thick strips.
Heat tortillas one at a time in a pre-heated skillet. Wrap in aluminum foil to keep warm.
Spoon 2 tablespoons farro onto each tortilla. Top with mushrooms, chiles, salsa and cheese, dividing evenly. Drizzle with Cilantro-Lime Crema before serving, if desired.