Preheat the oven to 350°F. Peel the beets and cut into quarters. In a small bowl, toss with the garlic and 2 tablespoons olive oil and place in a baking dish. Cover with aluminum foil and roast for 30 minutes. The beets will be very tender when a small knife is inserted in the middle (be sure to test out a few larger pieces); if beets are not easily pierced, roast for an additional 10 to 15 minutes and test again.
Once the beets and garlic cool slightly, place them in a food processor and process until combined. Add the tahini, lemon juice, and salt and blend again, scraping any bits off the sides. Process again, pouring the remaining 1/4 cup olive oil in a slow stream into the food processor while the mixture is blending. Once all the ingredients are added, process for 3 minutes or until the mixture is very smooth. Transfer to a plate for serving or into a container and refrigerate.
To serve, sprinkle za’atar over the dip, add the crumbled feta cheese on top, and finish with a hefty splash of extra-virgin olive oil. Serve with pita for dipping.
