Start by gathering all your ingredients. Slice the chicken breasts into 1/4-inch slices, chop the onion, and prepare the vegetables by peeling and cubing the Yukon potatoes, slicing the carrots, and breaking the cauliflower into florets.
In a large skillet or wok, heat the olive oil over medium heat. Add the chopped onion, ginger, and minced garlic. Sauté for about 3-4 minutes, or until the onion becomes translucent and fragrant.
Add the sliced chicken to the skillet. Cook for about 5-7 minutes, stirring occasionally, until the chicken is no longer pink.
Stir in the cubed Yukon potatoes, sliced carrots, and cauliflower florets. Cook for another 5 minutes, allowing the vegetables to soften slightly.
Add the yellow curry paste to the skillet, stirring well to coat the chicken and vegetables. This will infuse them with that signature Thai flavor.
Pour in the coconut milk, soy sauce, fish sauce, lime juice, brown sugar, and add the bay leaf and dried basil. Stir everything together and bring the mixture to a gentle simmer.
In a small bowl, mix the cornstarch with a few tablespoons of water to create a slurry. Stir this into the curry to help thicken the sauce. Let it simmer for another 10 minutes, stirring occasionally, until the sauce has thickened and the vegetables are tender.
Finally, add the thawed petite peas to the skillet and stir to combine. Cook for an additional 2-3 minutes until the peas are heated through. Remove the bay leaf before serving.