Heat the olive oil in a large skillet over medium-high heat.
Add the sliced chicken, chopped onion, cubed potatoes, sliced carrots, and yellow curry paste; cook, stirring occasionally, until the chicken is no longer pink.
Add the cauliflower florets, grated ginger, and minced garlic; sauté for about 1 minute.
In a small bowl, whisk about 1 cup of the coconut milk with the cornstarch until smooth, then pour it into the skillet.
Add the remaining coconut milk, soy sauce, fish sauce, 2 tablespoons lime juice, brown sugar, bay leaf, and dried basil; stir to combine.
Bring the mixture to a boil, then reduce heat and simmer uncovered for 15–20 minutes, or until the potatoes are tender.
Stir in the thawed peas and cook about 1 minute until heated through; discard the bay leaf.
Taste and adjust consistency with a splash of water or chicken broth if desired, and add chili sauce to taste.
Serve garnished with additional lime juice, fresh basil, and cilantro as desired.
