Place the mushrooms on your work surface cap side down. Trim two sides off the caps in line with the stems (so that when you slice the mushrooms there will be no stemless slices).

Using a mandoline or a very sharp knife, cut the mushrooms into paper-thin slices, making sure to keep the stem section attached.

Brush one side of each slice of bread lightly with oil. Place the mushrooms in a row on the unoiled side of the bread, slightly overlapping, making 3 or 4 rows to cover the surface. (There should be about 18 slices total for each piece of bread with no gaps of bread showing through.) Dab the mushrooms with olive oil and sprinkle with salt.

Place the bread, mushroom side up, in a panini-style grill, and close the grill top over the bread, pressing the top of the grill down to slightly smash the bread. Grill for about 3 minutes on medium high, until the bread is golden brown and the mushrooms are sizzling and cooked through.