Spray a 24-cup mini muffin tin with non-stick cooking spray. Cut the puff pastry into 24 2-inch squares, spreading out pastry with a rolling pin to increase surface area if necessary. Press pastry squares into muffin cups. Prick the bottom of each pastry with a fork. Place muffin tin in refrigerator until ready to use.
Heat olive oil in a large skillet over medium to low heat and add the onions. Saute for 15 to 20 minutes, stirring frequently, until the onions are soft and there is almost no moisture remaining in the skillet. Add 1/2 teaspoon salt, 1/4 teaspoon pepper, the wine, and thyme and continue to cook for another 10 minutes, until the onions are lightly browned. Remove from the heat. Caramelized onions can be made up to 2 days ahead of time. Store cooled onions in an airtight container in the fridge. Bring to room temperature before using.
Preheat oven to 425 degrees.
In a food processor or with an electric mixer, blend cream cheese, feta, and garlic clove until smooth. Season to taste with salt and pepper. Place heaping teaspoons of cheese mixture into pastry cups. Top with another teaspoon of caramelized onions. Pastry bites can be assembled a few hours ahead of time, cover with plastic wrap and store in refrigerator.
Bake for 20 minutes, or until pastry is golden brown. Serve hot. Pastry bites can be baked 3 days ahead of time. Reheat at 350 degrees for 5-7 minutes, or until hot.