Step 1

Purée ½ small red onion, 3 green Thai chiles or small serrano chiles, 2 garlic cloves, finely grated, one ½" piece ginger, peeled, finely grated, 1½ cups (packed) cilantro leaves with tender stems, 1 cup (packed) mint leaves, 2 Tbsp. fresh lemon juice, 2 tsp. Diamond Crystal or 1¼ tsp. Morton kosher salt, 1 tsp. sugar, and ¼ cup water in a blender until smooth. Transfer to a small bowl and set aside until ready to serve.

Step 2

Toast 2 tsp. cumin seeds in a dry small skillet over medium heat, shaking pan occasionally, until slightly darkened in color and very fragrant, about 2 minutes. Transfer to a spice mill or mortar and pestle and let cool, then finely grind.

Step 3

Heat ⅔ cup mustard oil* or vegetable oil in a small saucepan over medium-high until shimmering. Immediately pour into a heatproof medium bowl; let cool until lukewarm. (Heating mustard oil reduces its pungency.) Stir in cumin, 1 Tbsp. plus 1 tsp. Diamond Crystal or 2¼ tsp. Morton kosher salt, 2 tsp. cayenne pepper, 2 tsp. garam masala, and 1 tsp. ground turmeric to combine, then whisk in 3 garlic cloves, finely grated, one 2" piece ginger, finely grated, 1 cup plain whole-milk Greek yogurt, and 2 tsp. ajwain seeds or caraway seeds. Add four 6-oz. blocks paneer, cut into 4 cubes each to marinade and toss gently to coat. Let sit at room temperature 30 minutes.

Step 4

Prepare a grill for medium heat; oil grate with vegetable oil. Remove paneer from marinade, letting excess drip back into bowl, and thread onto skewers (3 or 4 cubes per skewer); discard marinade. Grill, brushing with vegetable oil and turning halfway through, until grill marks appear, 6–8 minutes total. If paneer sticks to grate, use a metal spatula to gently release.

Step 5

Line a platter with lettuce leaves; arrange skewers on top. Drizzle paneer with reserved chutney and sprinkle with chaat masala (if using). Serve with lime wedges for squeezing over.Do Ahead: Paneer can be marinated 2 days ahead. Cover and chill.