Prepare a medium-hot fire in a charcoal grill with a cover, or preheat a gas grill to medium-high.

Place the thawed pulp in a non-reactive (stainless steel or anodized aluminum) 3-quart fire-proof saucepan. Add the brown sugar, cumin, cayenne, and salt and mix well. Place the pan on the grill and let the mixture simmer for 10 to 15 minutes, stirring occasionally. The mixture will thicken and result in about 1 cup of sauce. Transfer the sauce to a small glass bowl and let it cool.

Place the ginger and garlic in the bowl of a food processor. Pulse a few times until finely chopped.

Place the oil in a medium-sized nonstick fire-proof skillet. Place the skillet on the grill and let heat for a few minutes. Transfer the chopped garlic and ginger to the skillet and cook, stirring occasionally, until golden brown, just a few minutes. Add the garam masala and cayenne and cook until the mixture turns brown. Remove from the heat and set aside to cool for a few minutes. Add the salt and mix well. Transfer the spice mixture to a large bowl. Add the beef and mix well. Divide the mixture into 6 equal portions and form 6 patties. Transfer the patties to a large baking dish and refrigerate.

Combine the onion, tomatoes, mint, salt, and lemon juice in a medium-sized glass bowl, mix well, and refrigerate.

When the grill is ready, brush the grill rack with oil. Place the patties on the rack, cover, and grill for 3 to 4 minutes. Turn the patties over, cover, and grill for another 3 to 5 minutes or until done to your liking. Transfer the patties to a serving platter.

Brush the cut sides of the buns with oil and grill them until lightly browned, 1 to 2 minutes.

To assemble the burgers, place enough lettuce to cover the browned side of the bottom buns. Spread about 2 tablespoons of the sauce on each of them. Add the patties and then add a few tablespoons of relish on each patty. Add the top buns and serve.