Shake the can of coconut milk or stir it well (this creates a consistent thickness, since the fat often solidifies at the top of the can).
In a 3- to 4-quart saucepan or wok over medium heat, simmer 1/2 cup of the coconut milk, stirring occasionally, until reduced by about half, 3 to 5 minutes. It will get very thick and shiny and may or may not separate; either is fine.
Add the curry paste, whisk well, and cook, continuing to whisk, for 1 minute. Whisk in the broth, sugar, fish sauce, and remaining coconut milk. Bring to a simmer over medium-high heat.
Add the pork, carrots, lemongrass pieces, and ginger slices and continue to simmer, adjusting the heat as necessary. After 2 minutes, add the bell peppers and baby corn and continue to simmer. After another 2 minutes, add the bamboo shoots and simmer until everything is tender and cooked through, about 1 minute more.
Remove the curry from the heat. Season to taste with more sugar and fish sauce. Transfer to a serving bowl (or serve right out of the pot). Remove the lemongrass pieces and ginger slices or tell your guests to eat around them. Garnish with the lime wedges, coconut milk, and red chiles.
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