Start by mixing all the ingredients for the stir fry sauce in a small bowl and set it aside.
Using a mortar and pestle or a food processor, grind the garlic and chopped red chili into a coarse paste. Put this mixture aside for later use.
For fresh rice noodles, either microwave or steam them for 2-3 minutes until they are warm and can be easily separated. Split each rice noodle roll vertically into halves using your hands or clean scissors, making them easier to eat. If using fresh noodle sheets, slice them into 1-inch wide strands. (Refer to the Notes section for using dried rice noodles).
Heat a wok or a large skillet over medium-high heat and add 1 tablespoon of oil. Once the oil is hot, add the sliced chicken thighs, spreading them apart quickly. Fry until the chicken is thoroughly cooked. Remove the chicken from the pan and set it aside.
Lower the heat to medium and add the chili garlic paste and julienned carrots to the pan, cooking for 20-30 seconds. Move this mixture to the side of the pan.
Raise the heat back to medium-high and pour the remaining oil into the empty space of the pan. Add the rice noodles and the prepared noodle sauce.
Gently toss the noodles until they are evenly coated with the sauce. Allow the noodles to sit undisturbed in the pan for 30-45 seconds or longer to achieve a charred flavor.
Add the Chinese broccoli and gently toss with the noodles. Cook until the greens have slightly softened.
Finally, add the cooked chicken and holy basil. Gently mix everything together. Remove the pan from heat and enjoy your delicious Thai Drunken Noodles!