In the bowl of the food processor, add the jalapenos, cilantro stems and leave, smashed garlic, fish sauce, canola oil, sesame oil, and sea salt. Pulse a few times until the mixture is fully combined. Put the chicken breasts into the plastic bag and pour in the marinade. Squeeze all the air out of the bag and mush the chicken around until all the pieces are coated in the marinade. Chill in the refrigerator until ready to grill, up to 8 hours.
In the small sauce pan, simmer the rice-wine vinegar, sugar, and salt for about 2 minutes. Pour the mixture into another small bowl or glass measuring cup and set aside until cool. Stir in the minced red pepper flakes, minced garlic, chopped cilantro, and water.
Grill the chicken over medium to high heat about 6 to 8 minutes per side. Slice and serve hot with the dipping sauce.