Preheat oven to 425 degrees F.
Cut eggplant in half and score flesh in a crisscross pattern. Drizzle 1 tablespoon oil and season with salt and pepper. Wrap eggplant in foil and place on baking sheet. Roast for 30 minutes or until tender.
Remove foil and scoop out flesh with a spoon into a strainer. Let sit for 10 minutes to remove excess moisture.
Mash black garlic and eggplant until well incorporated. Add tahini, lemon juice, and cumin, stirring to combine. Slowly add 2 tablespoons olive oil while whisking eggplant. Stir in yogurt and season with salt and pepper. Set aside.
Make salsa verde. Combine chopped parsley with olive oil, garlic, ground fennel, coriander, red pepper flakes, and lemon juice. Season with salt and pepper and set aside.
Heat honey in a small saute pan over medium heat until it comes to a simmer. Add red chili flakes, stirring to combine. Remove from heat.
Heat 2 tablespoons oil in a large saute pan over medium-high heat. Add mushrooms, giving them plenty of space in between and cook until seared, about 4-5- minutes. Flip and sear on the other side, about 3 minutes. Season with salt and pepper and keep warm.
Wipe pan clean. Lay halloumi slices in pan and cook until golden brown, about 3 minutes. Flip and cook until golden brown on the other side, about 2 minutes. Remove from heat. Drizzle hot honey on top.
Spread creamy black garlic babaghanoush on serving platter. Arrange mushrooms and halloumi on top and drizzle salsa verde. Serve immediately.