Look for dried rice vermicelli in the Asian section of your supermarket. We prefer the more delicate springiness of vermicelli made from 100 percent rice flour to those that include a secondary starch such as cornstarch. If you can find only the latter, just cook them longer—up to 12 minutes. For a less spicy sauce, use only one-quarter of the Thai chile. For the cilantro, use the leaves and the thin, delicate stems, not the thicker ones close to the root. To serve, place platters of noodles, salad, sauce, and pork patties on the table and allow diners to combine components to their taste. The sauce is potent, so use it sparingly.
1. FOR THE NOODLES AND SALAD: Bring 2 quarts water to boil in large pot. Stir in noodles and cook until tender but not 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 platter and refrigerate until needed.
2. FOR THE SAUCE: Using mortar and pestle (or on cutting board using flat side of chef's knife), mash Thai chile, 1½ teaspoons sugar, and garlic to fine paste. Transfer to medium bowl and add hot water and remaining 1 tablespoon sugar. Stir until sugar is dissolved. Stir in fish sauce and lime juice. Set aside.
3. FOR THE PORK PATTIES: Combine shallot, fish sauce, sugar, baking soda, and pepper in medium bowl. Add pork and mix until well combined. Shape pork mixture into 6 patties, each about 2½ inches wide and ½ inch thick.
4A. 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 half of grill. Set cooking grate in place, cover, and open lid vent completely. Heat grill until hot, about 5 minutes.
4B. FOR A GAS GRILL: Turn all burners to high, cover, and heat grill until hot, about 15 minutes. Leave all burners on high.
5. Clean and oil cooking grate. Cook patties (directly over coals if using charcoal; covered if using gas) until well charred, 3 to 4 minutes per side. Transfer grilled patties to bowl with sauce and gently toss to coat. Let stand for 5 minutes.
6. Transfer patties to serving plate, reserving sauce. Serve noodles, salad, sauce, and pork patties separately.