In a medium microwave-safe bowl, combine oil, garlic, and pepper flakes. Microwave, uncovered on high power, until garlic is golden brown and crispy, about 2 minutes, stirring halfway through. Set a fine-mesh strainer over a medium bowl and strain garlic oil through. Reserve infused oil and crispy garlic with pepper flakes separately.

In a separate medium bowl, whisk to combine yogurt, mint, cilantro, or basil, 1 tablespoon garlic-infused oil, lemon zest and juice, cumin (if using), and ¼ teaspoon salt, plus more to taste; Set aside while preparing eggplant.

For a Charcoal Grill: Open bottom vent completely. Light large chimney starter filled with charcoal briquettes (6 quarts). When top coals are partially covered with ash, pour evenly over grill. Set cooking grate in place, cover, and open lid vent completely. Heat grill until hot, about 5 minutes.

For a Gas Grill: Turn all burners to high, cover, and heat grill until hot, about 15 minutes. Leave all burners on high.

Clean and oil cooking grate. Brush eggplant all over with 3 tablespoons reserved garlic-infused oil and sprinkle evenly with ½ teaspoon salt and ¼ teaspoon pepper. Arrange eggplant on grill and cook (covered if using gas) until browned and tender, about 4 minutes per side. Transfer to platter. Brush with remaining 2 tablespoons strained garlic oil. Serve eggplant with yogurt sauce. Sprinkle eggplant and sauce with reserved crispy garlic.