Wrap the eggplant in aluminum foil. Set the eggplant and garlic cloves on a baking sheet and bake for 30 to 45 minutes, or until eggplant and garlic cloves have softened. The garlic may be done before the eggplant, so just take it out when you see fit.
Let eggplant cool for just a moment, or until you can safely touch it. Carefully peel off skin and add eggplant to a medium bowl. Push out garlic from skins and add to bowl as well.
Mix in salt, pepper, olive oil, sesame seeds, and lemon juice. Using a potato masher, mash ingredients together until well combined. If you like your dip a bit smoother, you can even use an immersion blender instead of a potato masher. But me, I like the texture of having a few chunks in the dip, so I stuck with the masher.