Heat the olive oil in a large skillet over medium heat. Add the chopped onion and sauté until it becomes translucent, about 3-4 minutes.
Add the sliced chicken breasts to the skillet. Cook until the chicken is no longer pink, about 5-7 minutes.
Toss in the cubed Yukon potatoes, sliced carrots, and cauliflower florets. Stir well to combine and cook for an additional 5 minutes.
Add the yellow curry paste to the skillet, mixing it in well with the chicken and vegetables.
Add the freshly grated ginger and minced garlic to the skillet. Stir well to combine and let the mixture cook for 1-2 minutes.
Pour in the coconut milk and stir to combine.
Add the cornstarch, soy sauce, fish sauce, lime juice, brown sugar, bay leaf, and dried basil. Stir until everything is well incorporated.
Bring the curry to a gentle simmer, then reduce the heat to low. Cover the skillet and let it cook for about 20 minutes.
In the last few minutes of cooking, stir in the thawed petite peas.
Serve the Thai Yellow Curry Chicken hot, garnished with fresh basil and cilantro.