Step 1

Pulse lemongrass, ginger, and garlic in a food processor until very finely chopped.

Step 2

Heat oil in a large heavy pot over medium heat. Add lemongrass mixture and cook, stirring often, until golden brown, about 5 minutes; season with salt. Add curry and tomato pastes and cook, stirring, until darkened, about 3 minutes. Add tomatoes and cook, scraping up any browned bits, until thickened, about 5 minutes. Stir in coconut milk; season with salt. Bring to a boil; reduce heat and simmer, stirring occasionally, until curry is rich and full of flavor, 20–25 minutes.

Step 3

Add sweet potatoes and carrots, then pour in water to cover. Partially cover pot and cook until carrots are crisp-tender, 10–15 minutes. Add shallots and cook until potatoes are tender and shallots are soft, 15–20 minutes.

Step 4

Add chile, if desired, and lime juice to curry and spoon over rice. Top with scallions, basil, and cilantro; serve with lime wedges.

Step 5

DO AHEAD: Curry can be made 2 days ahead. Let cool; cover and chill.