Preheat oven to 400F. Trim off and discard the stem end of eggplant and cut in half lengthwise. Place cut-side down on a baking sheet lined with a silicone liner or parchment paper. Pierce the backs of the eggplant with a fork in a few places. Bake until completely soft and somewhat collapsed, about 30 minutes. Remove from oven and allow to cool completely. This can be done ahead of time and stored in the refrigerator until ready to use.
At least 2 hours before using (and up to overnight), place almonds in a bowl and cover completely with water. Allow to soak at room temperature. Drain water before using.
Just Before Serving:
Put the almonds, sun-dried tomatoes, and garlic into food processor and pulse to chop. Peel the eggplant and add it, the basil, and the nutritional yeast to the processor and process to a coarse puree. Add salt to taste and pulse to blend.
Add a tablespoon to a serving of warm pasta (if the pesto is too thick to easily coat the pasta, add a little hot water to it), or use as a spread for bread or a dip for crackers or vegetables. Store in a covered container. For best color, either press a sheet of plastic wrap onto the exposed surface or spray with a light film of olive oil.