Break the feta into chunks and add to a food processor along with the cream cheese. Pulse until the cheeses are combined but still slightly chunky.
Add the Greek yogurt, minced garlic, lemon juice, honey, red pepper flakes, and oregano to the processor. Season with a small pinch of salt and freshly ground black pepper. Pulse again until combined but not completely smooth.
Roughly chop the roasted red peppers and add them to the mixture. Pulse just 3-4 times to incorporate them while leaving visible pieces throughout the dip.
With the processor running, slowly drizzle in the olive oil until the mixture becomes light and airy.
Transfer the dip to a serving bowl, cover, and refrigerate for at least 30 minutes to allow flavors to meld. Before serving, bring to room temperature for about 15 minutes, drizzle with additional olive oil, and garnish with fresh herbs and an extra sprinkle of red pepper flakes.