Heat the oven to 375ºF. Cut ½ inch from the top of the head of garlic to expose the cloves. Place the head on a sheet of foil and drizzle 1 teaspoon of the olive oil into the top. Wrap the garlic in the foil and bake until soft, about 45 minutes. Remove and let it cool.
When ready to serve, dredge the flatbreads in 3 tablespoons of the olive oil on a large baking sheet until coated on both sides. Transfer them to a cutting board and sprinkle with the thyme and ½ teaspoon of the salt. Stack the flatbreads and cut the stack like a pizza into 16 wedges (64 wedges total). Transfer the wedges to the baking sheet, arrange them in a single layer, and bake until crisp and lightly browned, 8 to 10 minutes.
Meanwhile, squeeze the head of garlic to release the roasted cloves into a food processor. Add the chickpeas (with the canning liquid), tahini, lemon juice, sesame oil, cumin, and remaining 2 tablespoons of olive oil and ½ teaspoon of salt. Process until smooth. Serve the dip with the flatbread chips.
Tip: Roast the garlic up to 3 days ahead of time and keep it refrigerated, wrapped in the foil, until you’re ready to use it.