In the bowl of a food processor, combine the drained white beans, chopped garlic, lemon juice, olive oil, dried thyme, salt, and pepper.
Purée the mixture until it is completely smooth and creamy, scraping down the sides of the bowl as needed.
Add the chopped olives and fresh parsley to the food processor.
Pulse the mixture for about 5 seconds, just enough to incorporate the olives and parsley without fully blending them in.
Taste and adjust seasoning if necessary.
Transfer the spread to a serving bowl. For best results, cover and refrigerate for at least 30 minutes to allow the flavors to meld and deepen before serving.