1. Prepare grill.
2. For the mushroom marinade, combine first listed amount of olive oil, lemon juice, garlic, mustard, salt, and black pepper in a medium bowl. Mix well.
3. Lay mushrooms on a flat pan and pour marinade over them. Gently toss mushrooms to coat completely, using a brush if necessary.
4. Carefully place mushrooms on the hot grill, top-side down. Grill for about 4 minutes, then gently turn and grill another 3 minutes. Move mushrooms to the cooler part of the grill so they will cook a bit more slowly and turn them top-side down again. Let cook for another 4 minutes. Mushrooms will darken and shrink as they finish. Remove from grill and let sit for about 20 minutes or until they're room temperature. Mushrooms will give off a fair amount of liquid during cooling.
5. With a very sharp knife, slice the mushrooms very thinly, at a slight angle.
6. Slice the baguettes into 1/2-inch slices and place on grill for about a minute. Place two to three mushroom slices on each slice of bread. Transfer the slices to a platter. Drizzle second listed amount of olive oil over the mushrooms. Sprinkle with the Asiago cheese and the flat-leaf parsley. To finish, add a few grindings of black pepper.
Source: Hannaford fresh Magazine, July - August 2006