Oil a medium bowl or gelatin mold, then line with plastic wrap for easy removal.
In a food processor, blend feta, butter, cream cheese, garlic, shallot, vermouth, and white pepper until smooth.
Layer ingredients into the mold as follows: ½ each of the pesto, pine nuts, sun-dried tomatoes, and cheese mixture. Repeat layers once more. Pat down to press ingredients into the mold, and refrigerate for at least 1 hour before serving.
Turn the dip out onto a serving plate, remove the plastic wrap, and serve.
