Preheat the oven to 425.
Trim the end of the eggplant, and if it is large, cut it in half lengthwise. Slice into 1/8-inch slices.
Put the parchment paper on the cookie sheet, then arrange the eggplant in a single layer. Lightly oil and bake for 8 minutes, until just starting to brown.
Flip each slice and bake another 3 minutes, until each slice is an uneven mix of colors, from pale to almost burnt. Transfer to a plate and set aside.
Lower oven to 350.
Combine soy sauce and liquid smoke in the bowl, then dip each piece of eggplant in it and place back on parchment paper.
Bake for 3 minutes, until hot.