If serving the dip in Spanish-onion "bowls": Preheat oven to 350 degrees. Cut the top third off each onion, and discard. Trim bottoms so that onions are level when set in a baking dish. Drizzle with some olive oil; season with salt. Bake until soft, 1 to 1 1/4 hours. When onions are cool enough to handle, pull out and discard all but the outermost 2 or 3 layers. Set "bowls" aside.
Heat olive oil in a medium heavy-bottomed pot over medium-high until hot but not smoking. Cook sliced onions, stirring occasionally, until soft and golden brown, about 15 minutes. Cover; reduce heat to low. Cook, stirring occasionally, until caramelized, about 40 minutes.
Raise heat to medium, and season onions with salt. Stir in vinegar; simmer until mixture is dry. Stir in thyme; remove from heat. Let cool; coarsely chop onions.
With an electric mixer, beat cream cheese in a medium bowl until smooth. Fold in sour cream and caramelized onions with a rubber spatula; season with salt and pepper. Divide dip among onion "bowls," or transfer to a dish. Cover with plastic wrap, and refrigerate 1 hour.
Make garnish if desired: Heat the safflower oil in a medium skillet over high until hot. Thinly slice the remaining small onion, and fry in small batches until crisp, about 1 minute. Drain on paper towels. Garnish with crisp onions; serve with roasted fingerling potato crisps if desired.