Prepare a charcoal or gas grill for medium-high heat. Place eggplants directly on coals or over grill grates. Cook, turning occasionally, until skins are completely charred and flesh collapses, about 15 minutes. (Alternatively, you can cook eggplants directly on the grate of your oven at 450*F for 30 minutes, rotating once halfway through.) Transfer to a cutting board and let cool.
Meanwhile, cook garlic in remaining 2 Tbsp. oil in a small skillet over medium-low, shaking pan occasionally, until garlic turns golden, about 4 minutes. Transfer garlic to a paper towel and reserve oil.
Remove skins from eggplants and place flesh in a food processor. Pulse 5 to 7 times, or until eggplant is finely chopped. Place in a bowl and mix in 3 Tbsp olive oil, coconutmilk yogurt alternative, tahini, lemon juice, red pepper flakes, and salt.
Transfer dip to a bowl and top with garlic and herbs. Drizzle garlic-infused olive oil over dip and serve with warm pita, crudités, and/or chips.