Prepare the Aromatics: Garlic and ginger get minced finely so they melt into the sauce. Lemongrass gets gently crushed with the back of a knife to release aroma. Kaffir lime leaves stay whole so they infuse flavor slowly.
Start the Curry Base: Olive oil gets heated over medium heat in a deep pan. Garlic and ginger go in first and get stirred until fragrant. Red curry paste gets added next and cooked briefly so the oils release and deepen the color.
Build the Sauce: Sugar gets stirred into the curry paste, followed by coconut milk and chicken broth. Everything gets mixed gently until smooth. Lime leaves and lemongrass go in and the sauce starts to simmer softly.
Cook the Chicken: Chicken pieces get added directly into the simmering sauce. They get stirred so each piece gets coated. Cooking continues until the chicken turns tender and fully cooked through.
Add the Vegetables: Snow peas get stirred in near the end so they stay bright and slightly crisp. The curry simmers just a few more minutes while flavors come together.
Finish and Taste: Salt and black pepper get adjusted to taste. Lemongrass stalks and lime leaves get removed before serving. Fresh cilantro gets sprinkled on top right at the end.
