Step 1
Place a rack in center of oven; preheat to 400°. Toss 1 lb. skinless, boneless hen breasts (about 2 medium) with 1 Tbsp. inexperienced curry paste, 1 Tbsp. vegetable oil, and 1 tsp. Diamond Crystal or ½ tsp. Morton kosher salt on a big rimmed baking sheet till evenly coated. Bake till hen is opaque and simply cooked by means of (an instant-read thermometer inserted within the thickest a part of a breast ought to register 150°), 15–20 minutes. Set hen apart; go away oven on.
Step 2
Warmth 4 Tbsp. unsalted butter in a big Dutch oven or different heavy pot over medium. Add 1 massive onion, lower into ½” items, 1 massive or 3 medium carrots, peeled, halved lengthwise, thinly sliced, 3 child Yukon Gold potatoes, scrubbed, quartered, thinly sliced, and 4 garlic cloves, finely chopped. Cowl and prepare dinner, stirring often, till onion is translucent and carrots are starting to melt, 8–10 minutes. Sprinkle ¹⁄₃ cup all-purpose flour over and prepare dinner, stirring consistently, till flour is pale golden, about 5 minutes.
Step 3
Add remaining 3 Tbsp. inexperienced curry paste and 1¾ cups water to pot; stir to mix. Carry combination to a boil, scale back warmth, and simmer, stirring consistently, till sauce may be very thick and potatoes are almost tender, 6–8 minutes. Stir in ½ cup heavy cream and produce to a simmer; take away from warmth.
Step 4
Switch reserved hen to a chopping board and lower into ½” items. Add to filling in pot together with 1 cup frozen inexperienced peas, 2 Tbsp. contemporary lime juice, 1 Tbsp. fish sauce, and 1 tsp. sugar; stir to mix. Style filling and season with salt if wanted. Scrape into an 8×8″ baking dish or a 9″-diameter deep glass pie dish; clean floor.
Step 5
If utilizing a 14-oz. package deal of frozen puff pastry, lower dough in half and gently roll out 1 half on a frivolously floured floor simply to clean any creases and make barely bigger than the baking dish; reserve remaining half for an additional use.
Step 6
If utilizing a 17.3-oz. package deal of frozen puff pastry, gently roll out 1 sheet on a frivolously floured floor to clean out any creases and make barely bigger than the baking dish.
Step 7
Flippantly brush puff pastry with cream, then punch out a 1″-diameter spherical from the middle with a small cutter or bottle cap (or lower out with a paring knife). Drape pastry over baking dish, letting it grasp a bit of over the sides (don’t crimp). Trim, leaving a couple of ¼” overhang if wanted.
Step 8
Place baking dish on a rimmed baking sheet (to catch drips) and bake pot pie till puff pastry is golden brown and filling is effervescent across the edges, 25–half-hour. Let cool 10 minutes earlier than serving.
