Mince cilantro stems and leaves. Peel, trim, and cut carrots into ½" diagonal slices. Slice thin rounds from pointed half of Fresno chile. Discard seeds if you prefer less spice. Stem and mince other half of Fresno chile.
Finish Preparing the Ingredients
Halve snow peas on an angle. Quarter lime. Rinse tilapia fillets, pat dry, and season both sides with ½ tsp. salt and a pinch of pepper.
Cook the Tilapia
Heat 2 tsp. olive oil in a large non-stick pan over medium-high heat. Place tilapia in hot pan. Cook until browned and tilapia reaches a minimum internal temperature of 145 degrees, 3-4 minutes per side. Remove tilapia to plate. Reserve pan; no need to wipe clean.
Start the Curry
Return pan used to cook tilapia to medium-high heat. Add 1 tsp. olive oil and carrots to hot pan and cook, undisturbed, until lightly charred, 1-2 minutes. Add ginger, lemongrass, and minced Fresno (to taste). Cook, stirring constantly, until fragrant, 30 seconds. Stir in coconut milk, curry paste, and 1 cup water and bring to a simmer. Simmer, stirring occasionally, until carrots are tender, 3-4 minutes.
Finish the Curry
Remove pan from burner. Stir in snow peas and half the cilantro (reserve remaining for garnish). Using a fork or your hands, flake tilapia into bite-sized pieces. Add flaked tilapia to pan. Season with ½ tsp. salt and ¼ tsp. pepper.
Plate the Dish
Scoop a serving of curry into a shallow bowl and garnish with remaining cilantro and Fresno rounds (to taste). Serve with lime wedges.