Step 1
If using 16 head-on tiger prawns, working 1 prawn at a time, snip off antennae and legs with kitchen shears, then cut through shells along length of backs just deep enough into flesh to expose veins; remove veins and discard. Run a paring knife along backs of prawns, cutting most of the way through, and open up flesh like a book.
Step 2
Mix grated 3 garlic cloves, finely grated, one 2″ piece ginger, peeled, finely grated, and 1 Tbsp. fresh lemon juice in a medium bowl; season with kosher salt. Add prawns (or 16 deveined peeled extra-jumbo shrimp) and toss gently to coat. Cover and chill at least 20 minutes and up to 4 hours.
Step 3
Mix 1 cup plain whole-milk Greek yogurt, 2 Tbsp. cream cheese, room temperature, 2 tsp. Kashmiri chile powder or paprika, 1 tsp. ajwain seeds or caraway seeds, 1 tsp. garam masala, 1 tsp. ground turmeric, 5 garlic cloves, finely chopped, 1½ tsp. Diamond Crystal or 1 tsp. Morton kosher salt, and remaining 4 Tbsp. fresh lemon juice in another medium bowl to combine.
Step 4
Remove prawns from lemon juice marinade; discard. Transfer to yogurt marinade; toss to coat. Cover and chill at least 30 minutes and up to 2 hours.
Step 5
Prepare a grill for medium heat; oil grate. Arrange prawns, butterflied side up, on grate and grill, undisturbed, basting often with melted unsalted butter, until flesh is opaque throughout and shells are bright orange, about 5 minutes. (For shrimp, thread onto skewers and grill, turning once and basting often on both sides, until opaque, about 5 minutes.)
Step 6
Divide prawns among plates or transfer to a platter; top with cilantro leaves and store-bought fried garlic (if using). Serve with lime wedges for squeezing over.
