Combine crumbled feta, softened cream cheese, ¼ cup yogurt, 1½ tablespoons oil and grated garlic in a food processor; process until a smooth whipped dip forms, 2 to 4 minutes, stopping to scrape down sides as needed. Transfer to a serving bowl.
Arrange quartered beets over the whipped feta. Sprinkle with chopped pistachios and drizzle with 1 tablespoon honey. Sprinkle with 1 tablespoon dill and ½ teaspoon Aleppo pepper, if using.
