Spread the yogurt to 1/2-inch thickness onto several layers of heavy-duty paper towels. Top the yogurt layer with additional paper towels. Allow the yogurt to dry for 5 minutes.
Using a rubber spatula, remove the yogurt from the paper towels and place in a food processor with the cheeses, sour cream, and garlic. Blend until smooth.
Scoop the blended yogurt into a medium serving bowl, and add the spinach, minced dill, and pepper. Cover the dip and refrigerate for 1 hour. If desired, garnish with fresh dill prior to serving.
