FOR THE NOODLES AND SALAD: Bring 4 quarts water to a boil in large pot. Stir in noodles and cook until tender but not too mushy, 4 to 12 minutes. Drain noodles and rinse under cold running water until cool. Drain noodles very well, spread on large plate, and let stand at room temperature to dry. Arrange lettuce, cucumber, cilantro, and mint separately on large platter and refrigerate until needed.

FOR THE SAUCE: Using mortar and pestle (or on cutting board using flat side of chefs knife), mash Thai chile, 1 tablespoon sugar, and garlic to fine paste. Transfer to medium bowl and add hot water and remaining 2 tablespoons of sugar. Stir until sugar is dissolved. Stir in fish sauce and lime juice. Set aside.

FOR THE PORK PATTIES: Combine shallot, fish sauce, sugar, baking soda, and pepper in a medium bowl. Add pork and mix until well combined. Shape pork mixture into 12 patties, each about 2 1/2 inches wide and 1/2 inch thick.

FOR 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. Cook patties until well charred, 3 to 4 minutes per side. Transfer grilled patties to bowl with sauce and gently toss to coat. Let stand 5 minutes.

Transfer patties to serving plate, reserving sauce. Serve noodles, salad, sauce, and pork patties separately.