Add cream cheese, feta, olive oil, and lemon juice.
Pulse until smooth. You may want to do this in two batches if you find the feta is not blending.
Add the lemon zest, thyme, salt, pepper and red pepper flakes and pulse again.
Pour dip into a serving bowl.
Drizzle with olive oil and sprinkle additional thyme leaves on top.
Serve with pita, bread rounds and cut up vegetables.
Notes
If you want to make this ahead don't add the drizzle of olive oil. The cheeses will harden in the refrigerator so you may want to throw it back into the food processor or blender to whip it again before serving.
Nutritional information is provided as a courtesy and is an estimate only. This information comes from online calculators. Although attempts have been made to provide accurate nutritional information, these figures are only estimates.