Thai Green Curry with Shrimp, Snow Peas, and Shiitakes

2 (14-ounce) cans coconut milk

2 tablespoons Thai green curry paste

2 tablespoons fish sauce

2 tablespoons packed brown sugar

1 1/2 pounds extra-large shrimp (21 to 25 per pound), peeled, deveined, and tails removed

5 ounces shiitake mushrooms, stemmed and halved if small or quartered if large

4 ounces snow peas, strings removed

1 red bell pepper, stemmed, seeded, and cut into 1⁄4-inch-wide strips

1 Thai chile, stemmed, seeded, and quartered lengthwise (optional)

1/4 cup coarsely chopped fresh basil leaves

1/4 cup coarsely chopped fresh mint leaves

1 tablespoon lime juice

Salt

Carefully spoon off about 1 cup of top layer of cream from 1 can of coconut milk. Whisk coconut cream and curry paste together in Dutch oven. Bring to simmer over high heat and cook until almost all of liquid has evaporated, 5 to 7 minutes. Reduce heat to medium high and continue to cook, whisking constantly, until oil separates from solids and mixture is darkened and aromatic, 4 to 8 minutes.

Whisk in remaining coconut milk, fish sauce, and sugar. Bring to simmer and cook until flavors meld and sauce is thickened, about 5 minutes. Stir in shrimp and mushrooms and cook for 5 minutes. Stir in snow peas, bell pepper, and Thai chile, if using, and cook until vegetables are crisp-tender, and shrimp are opaque throughout, about 2 minutes. Off heat, stir in basil, mint, and lime juice. Season with salt to taste. Serve.