Cut the eggplant lengthwise in half.
Score both halves on the flesh side, making a crisscross pattern and ¼ inch deep.
Sprinkle both halves with salt and place them scored side down on a baking sheet.
Cover with another baking sheet and place a heavy object (such as a set of bowls) on top. Let the eggplant render its excess liquid at room temperature for 1 to 2 hours.
Preheat the oven to 350°F.
Rinse the eggplant, pat dry, and rub with some olive oil.
Place the halves flesh side down on a lightly oiled baking sheet. Roast for about an hour, or until the eggplant is very soft and the skin is wrinkled; there should be no resistance when tested with a knife. Remove from the oven and let sit until cool enough to handle.
Scoop out the eggplant pulp and lightly chop it.
Place the pulp in a double layer of cheesecloth and tie it securely into a bundle with butcher's twine. Place the bundle in a colander set over a bowl and refrigerate. Let drain 2 hours, or overnight.
Remove the eggplant from the refrigerator and hold the bundle over the sink. Twist and squeeze the cheesecloth to remove as much additional liquid as possible.
Place the pulp (you should have about ½ cup) in a small food processor or mini-chop. Pulse a few times to begin breaking up the eggplant.
With the motor running, slowly pour 2 tablespoons of the olive oil through the feed tube. Continue blending for 30 seconds. The color and texture will begin to lighten.
Stop the machine and add the garlic, mustard, and salt to taste.
Blend again, then add the remaining 2 tablespoons olive oil. Continue processing for another minute, then taste and adjust the seasoning.
Cover and store in the refrigerator until ready to serve, or for up to 1 week.