For the sauce, in a small skillet over medium-high heat, combine the stock, ginger and crushed garlic; reduce by half. Remove the ginger and garlic and stir in the peanut butter to melt and incorporate. Add the the hoisin; remove from heat and stir in lime juice.
In a small bowl, season the cucumber with salt and sugar. Toss and let stand.
In a large skillet over high heat, heat the oil, two turns of the pan. When the oil ripples and smokes, add the chicken; brown and crumble. Add the ginger, garlic, pepper, mild peppers and chili peppers; stir 2 minutes to cook the peppers to tender-crisp. Add the basil, mint, fish sauce, lime juice and scallions; taste and adjust the flavors.
Serve in a large platter topped with peanuts, and with the lettuce platter and sauce alongside.