While the dough rests, heat 2 tablespoons of vegetable oil in your wok or large skillet over medium-high heat until it shimmers. Add the minced garlic, ginger, and Thai chilies, stirring constantly for about 30 seconds until fragrant but not browned. The kitchen should smell amazing right about now.
Add the ground chicken to the pan, breaking it up with a wooden spoon or spatula. Cook for 4 to 5 minutes, stirring occasionally, until the chicken is mostly cooked through and no longer pink. Don't worry about browning it perfectly at this stage.
Sprinkle the curry powder and turmeric over the chicken, stirring to coat everything evenly. Let the spices toast for about 1 minute until they become fragrant and deepen in color. This step is crucial for developing complex flavors rather than raw spice taste.
Stir in the soy sauce, fish sauce, and brown sugar, mixing well to combine. Add the diced carrots and the white parts of the green onions. Cook for 3 to 4 minutes until the carrots begin to soften but still have some bite.
Add the frozen peas and cook for another 2 minutes until heated through. Remove from heat and stir in the chopped cilantro and green parts of the green onions. Taste and adjust seasoning if needed. The filling should be savory, slightly sweet, with a pleasant heat. Set aside to cool slightly while you prepare the roti.